Friday, November 30, 2012

Atoms Part 1: How Atoms Are Made

The very first atom, a simple union of a proton with an electron, appeared when the universe was just about 380,000 years old. It was hydrogen.

Big Bang Synthesis

Just after the Big Bang, our universe started out as a tiny seething environment filled with unimaginable energy. In just a millisecond, tiny particles called quarks formed. They come in two stable kinds - called up and down. The temperature was several trillion degrees Celsius. These quarks, attracted to each other by a fundamental force in the universe, called the strong force, quickly formed little groups of three quarks each, called neutrons and protons. About seven times more protons were created than neutrons. Neutrons contain two down quarks and one up quark. Protons contain one down quark and two up quarks.

Free protons are very stable. Each one, made right after the Big Bang, will outlast our universe. But free neutrons are unstable. They have a half-life of just over 10 minutes. This means that of all free neutrons today, only half will remain 10 minutes from now. What happens to them? They decay into stable protons. A down quark decays into an up quark.

Few free neutrons had a chance to decay, however. A few seconds after the Big Bang, almost every free neutron was paired up with another neutron and two protons to make a helium-4 nucleus. Helium-4 nuclei are very strongly bound. The strong force again attracted them to each other just as it attracted quarks together. By the time the universe was about three minutes old, the process of making atomic nuclei had stopped altogether, and once bound inside nuclei, neutrons became stable.

The universe had enough time to make a handful of simple atomic nuclei: a lot of helium nuclei, along with trace amounts of deuterium and lithium nuclei. The majority of protons didn't bind into nuclei at all. They remained free instead. Around these protons and nuclei, electrons and photons zipped around in all directions. A photon is a particle of light and radiation. The universe had to cool down much more before electrons could settle into orbits around nuclei to create atoms. It took about 380,000 years. When the electrons settled into atoms, photons were freed up to fly away in all directions. This is where something you may have heard of, the cosmic background radiation, came from. These photons started off as highly energetic radiation called gamma rays. While they traveled, space itself expanded as the universe expanded. This expansion stretched their wavelengths longer. These photon travelers from that distant time reach us today as faint (long wavelength) microwave background noise. You can see it as snow on an old fashioned TV when it isn't tuned to any station.

Hydrogen is the lightest and simplest elemental atom in the universe. It is assigned the atomic number 1 because it has just one proton in its nucleus. Every single kind of atom, or element, has its own atomic number. This hints at something very important about atoms. The number of protons in an atom's nucleus determines what kind of atom it is - it is what makes iron, with 26 protons, different from copper, with 29 protons, for example:
Of all the mass of all the atoms in the universe, 75% comes from hydrogen. Before stars formed, the only atoms in the universe were hydrogen, helium and lithium:
The early atom picture is just a bit more complex than this, however. Each of these three kinds of atom comes in different types, called isotopes. To understand what an isotope is, let's take hydrogen as an example. The simplest hydrogen atom contains a nucleus made of just one proton. However, all atomic nuclei larger than this hydrogen atom also contain neutrons. The number of neutrons in an atomic nucleus determines which isotope it is.

The simplest isotope of hydrogen is hydrogen-1 or 1H. Other isotopes of hydrogen were also made when hydrogen-1 was made: hydrogen-2, called deuterium, and hydrogen-3, called tritium, for example:
Protons and neutrons (shown in orange and purple, respectively, in this diagrams) in a nucleus attract each other through a glue-like force called the nuclear strong force, but protons naturally repel each other because they are of the same positive charge. These two forces compete with each other. Neutrons tend to stabilize a nucleus because they attract each other and protons equally. Too many neutrons, however, can destabilize the arrangement. When an atomic nucleus takes on more and more neutrons, it tends to get more and more unstable. The nucleus becomes unwieldy. Deuterium, like hydrogen-1, is stable. These atoms, once they were formed billions of years ago never decay. Tritium, on the other hand, isn't stable. It is radioactive, and it has a half-life of about 12 years. This means that in 12 years, half of all tritium atoms today will have decayed into another, stable, atom called helium-3. An unstable tritium nucleus, with one proton and two neutrons, decays into a stable helium-3 nucleus, with one neutron and two protons. A neutron decays into a proton, releasing an electron in the process.

All the tritium in the universe would have disappeared billions of years ago if it were not made naturally when cosmic rays interact with gases. Neutron-heavy hydrogen-4, 5, 6 and even hydrogen-7 have been made in the lab, but they are very unstable isotopes and they last just tiny fractions of a second before decaying into more stable atoms.

Besides stable hydrogen-1 and deuterium, helium-3, helium-4 and lithium-7 atoms, all of which are also stable, were made when atoms began to form in the universe. Almost a quarter of the atomic mass of the universe is made up of helium-4, with trace amounts of deuterium, helium-3 and lithium-7. No other elemental atoms were made at this time. They didn't exist in the universe until the first stars formed about 200 million years later, and began to fuse lighter elements into heavier ones.

Star Core Synthesis

During most of a star's life, hydrogen fuses into helium under the enormous pressure and heat deep inside its core. Small stars, like our Sun, will eventually run out of hydrogen and nuclear fusion will stop. Only in very massive stars, much larger than our Sun, do carbon, oxygen and even iron atoms form in significant quantity, all from successive fusion reactions.

The production of carbon atoms requires even more energy than the fusion of hydrogen into helium. When a large star begins to run out of hydrogen, its core begins to collapse. This pressure heats it up even further. Helium nuclei begin to fuse fast enough to compete with the decay of their unstable product, beryllium-8. If they don't fuse fast enough, beryllium-8 simply decays back into two helium nuclei before any new fusion reaction can happen. Now, however, some beryllium-8 sticks around long enough to fuse with other helium nuclei. When they do, stable carbon-12 nuclei are created. Three helium nuclei fuse into a carbon nucleus. The two fusion reactions involved in making carbon occur almost simultaneously:

Carbon nuclei can fuse with other helium nuclei to create oxygen nuclei, and so on. Carbon atoms didn't form right after the Big Bang because the universe cooled down before carbon nuclei could form.

When we think about atomic nuclei fusing with each other to make bigger nuclei, we are describing a special high-energy environment inside a star. Here, the pressure and temperature are so high that atoms don't exist as atoms, with electrons orbiting nuclei. Here, the electrons are just too excited. They fly around freely. When this happens you get a special state of matter called plasma. Free nuclei float around in a "soup" of highly energized electrons flying around in all directions. This plasma within a star is similar to the plasma that filled the universe just before atoms formed.

In the plasma inside very large stars, all the available carbon nuclei eventually fuse into even larger nuclei such as oxygen, sodium and magnesium. Once the carbon is gone, the star contracts once again and gets even hotter. Oxygen fuses into silicon and sulfur nuclei as well as other elements. Eventually the core of the star contains nothing left but sulfur and silicon. It contracts further and it gets even hotter. It soon has enough energy to make even heavier elements. Each new nucleus is made by fusing a helium nucleus to an existing nucleus, in a step-by-step fashion. For example, a silicon nucleus fuses with a helium nucleus to make sulfur. The sulfur nucleus fuses with another helium nucleus to make argon. The argon nucleus fuses with another helium nucleus to make calcium, and so on. This process continues along to create larger and larger nuclei. It all happens very fast. The entire step-by-step process lasts about five days in total, until a nickel-56 nucleus is eventually made. Then it suddenly stops. This is when things get very interesting for the large star.

Stars burn brightly for many millions of years because massive amounts of energy are released every time light elements such as hydrogen fuse into helium. This energy is called nuclear binding energy. It's the energy needed to remove a proton or a neutron from a nucleus and it's the same energy that's released when a proton or a neutron is added to a nucleus.

As atomic nuclei get larger and larger, the increase in binding energy as protons and neutrons are added to the nucleus begins to wane, and eventually it doesn't increase at all. It becomes negative. The graph below charts binding energy as a function of nucleus size. Initially, as protons and neutrons are added to the nucleus, the binding energy of the nucleus increases dramatically. See the sharp upward incline to the left. You can see the increase start to wane at around carbon and oxygen nucleus size. (Notice the little jagged up-tick in energy at helium - this shows how much binding energy this particular nuclear arrangement has. This nucleus is especially tightly bonded together.) Now look at iron-56. This nucleus has the highest binding energy in this graph:

Actually, nuclei with 58 and 62 nucleons have the highest possible binding energy of all nuclei. We don't get them here in this massive star, because each new element must be a multiple of 4 (a helium nucleus has 2 protons and 2 neutrons). We get nickel-56 instead (that's 14 helium nuclei that have bound up together). As nickel-56 tries to fuse with one more helium nucleus to make the next largest element, zinc-60, the process actually requires energy instead of producing it. Rather than releasing energy when neutrons and protons are added, heavier elements release energy when protons and neutrons are removed ? fission rather than fusion is favoured. Nickel-56, therefore, is the last element this star or any star can make in its core.

With all this nickel being made, you may wonder why the cores of rocky planets and meteorites contain lots of iron-56 in them, not nickel. That's because nickel-56 is unstable. It has a half-life of about 6 days as it decays into cobalt-56, which is also unstable with a half-life of about 77 days. Cobalt-56 decays into iron-56, and that is a stable nucleus. It is the heaviest stable element made inside a star.

So what happens next when nickel-56 is made inside the star? And where do even larger atoms come from?

Supernova Synthesis

When stars are busy fusing nuclei, they are in a state of equilibrium. The outward force of thermonuclear fusion balances the inward force of gravity. When fusion reaches nickel-56 size, it stops altogether. The core begins to collapse once again but this time there's no new kind of fusion to ignite and restart the process. No more outward force is created to balance the crushing inward force of gravity. The star completely collapses in on itself. This collapse is catastrophic - it can reach a velocity as high as 70,000 km/second! The temperature and density of the core skyrocket. The inner core of the star eventually reaches a density comparable to that of an atomic nucleus. Consider that atoms are 99.9% empty space! Here, all that empty space has been squeezed out and atomic nuclei and electrons are packed in on each other. They are so tightly squeezed that protons begin to capture electrons and turn into neutrons. This process creates a dense hot neutron soup that can't decay any further. The temperature is about 6000 times higher than it was before the collapse. It is an environment where large and highly unstable neutron-rich nuclei form through a process called neutron capture, rather than through nuclear fusion. Free neutrons are basically squeezed into large nuclei so fast the nuclei don't have a chance to decay. There is an upper limit to nuclei formed this way. When the number of nucleons approaches 270 (that's larger than any even unstable atom scientists have created), the nucleus rapidly and spontaneously decays through fission, releasing a lot of energy, until it reaches a stable isotope.

The core collapses, creating a slew of new heavy unstable atoms all within a few seconds. The rapid collapse of the large star releases a staggering amount of gravitational potential energy. It is this energy that drives a supernova explosion. Heavy nuclei blow far and wide into surrounding space.

As the energy of explosion begins to subside, smaller unstable (radioactive) nuclei formed in the super-heated core undergo a series of nuclear decays (rather than fission) until they reach stable nuclei. Lead-204, with 82 protons and 122 neutrons, is the heaviest stable atomic nucleus in the universe. All elements in the periodic table with atomic numbers higher than 82 are unstable, although some of these have very long half-lives. Bismuth-209 for example, with 83 protons, has a half-life longer than the age of the universe, and therefore can be thought of for all intents and purposes as stable, and non-radioactive.

Every subsequent supernova seeds the universe with more and more large atomic nuclei. While the number of very small atoms remains about the same today as when they were created shortly after the Big Bang, the number of larger atoms continues to increase as they are created in the cores of large stars and during supernovae. These three kinds of atom creationBig Bang synthesis, star core synthesis and supernova synthesis - explain why there is so much hydrogen and helium in the universe, why there are significant amounts of oxygen, carbon and silicon - major components of rocky planets like Earth, and why heavy metals such as gold-79 (Au) and platinum-78 (Pt) are precious because they are present in the universe only in tiny amounts.

Next, take a look at Atoms Part 2, which explore how atoms emit light.

Thursday, November 29, 2012

Atoms Part 2: Atoms and Light

TV sets, the Northern Lights, fireflies and fireworks all have one thing in common: they emit light. The light comes from atoms. An atom can emit bright distinct colours.  How does an atom pull off this visually stunning trick?

Atomic Structure

Bright colourful displays of light owe themselves to the electrons in atoms - how they are arranged and how they move inside the atom.

Every atom comes in the same basic formula: protons, neutrons (except for hydrogen-1 which doesn't have one) and electrons. Below is a simple diagram of an oxygen-16 atom. Eight electrons surround a nucleus made up of eight protons and eight neutrons. The nucleus is drawn as a simple pink circle.

The atom is the basic building block of all matter in the universe, from gases, to liquids to solids. To form a nucleus, tiny fundamental particles called quarks bind together in groups of three to make protons and neutrons. Quarks come in six types but only two types - up and down quarks - are stable and make up atomic nuclei. Two up quarks and a down quark bind with each other through a fundamental glue-like force called the strong force to make a proton. Two down quarks and an up quark bind the same way to make a neutron. Protons and neutrons bind to each other inside a nucleus through the same strong force. As implied by the name, this force is strong. It won't let neutrons and protons budge unless enormous energy is applied to the atom.

The electrons in atoms are a different story. Electrons are attracted to the nucleus through a different fundamental force, called the electromagnetic force. This force is less intense. The electrons have a little wiggle room. An electron can absorb energy, either from colliding with another atom or by absorbing a tiny packet of light called a photon. An electron can move away from or closer to the nucleus depending on its energy. Negatively charged electrons are attracted to positively charged protons in the nucleus, but an electron will never fall or spiral down into the nucleus because it must maintain a specific minimum amount of energy. This minimum energy is based on the rules of quantum mechanics. In fact, the rules go even further: the electron not only has to maintain a certain minimum energy, preventing it from spiraling into the nucleus, it is also limited to specific values of higher energies too. Electron energy is quantized, which means it comes only in tiny specific amounts. It's like ordering coffee to go from a coffee shop - you can get a small, medium or large but not a med/large. That in-between price is not entered in the cash register.

An electron becomes excited when it absorbs energy.  When it is excited, it may move away from the nucleus a tiny bit. The distance it can move outward is, again, quantized into tiny packets, or specific distances. An electron might absorb a tiny amount of energy and still not become excited. It needs to absorb a specific amount of energy before it can move up into a higher energy state. It's like climbing the rungs of a ladder. Moving your foot up halfway between rungs won't get your body any higher up. To climb, you can move up only by the height of each rung, one rung at a time. I've redrawn the oxygen atom (right), this time adding two more rings in grey. These grey rings are two possible excited electron states. They are further away from the nucleus because they represent higher energy. Electrons can move into specific rings (distances) but not in between them.

Electrons Can Be Described As Wave Functions

The quantum mechanical arrangement of electrons in an atom is described by a complex mathematical formula called a wave function. What we need to know about the wave function is that, in a real atom, the exact locations of electrons can't be found; they can only be localized into clouds where they are likely to be found. These clouds are also called orbitals and they can take on some fairly complex shapes. It also means that you can measure the speed of an electron as it orbits in the atom, or you can measure its location, but you can't know both at the same time. Despite this uncertainty, you can describe the average distance of an electron from its nucleus. This is called an electron shell. It isn't a realistic description of how the electron moves around the nucleus, but it does give you an idea of how much average energy an electron possesses. Shells are represented by the rings around the nucleus like the ones we drew for the oxygen atom. Electron energy increases as you go outward in the rings. As a general rule, the innermost shell is filled with electrons first, before electrons occupy outer shells. This arrangement represents the lowest possible energy state, or ground state, of an atom. In the oxygen atom, the two black rings are ground state shells. Atoms, like all systems, tend to want to be in the lowest energy state possible.

Now I'll take a hydrogen atom, the simplest of all atoms, and use it to show you how it can emit light. Light emission from all other atoms works the same basic way. Here is what a simple electron shell diagram of a hydrogen atom looks like, right:

The electron in this atom is in its ground state; it occupies the closest possible electron shell. Although it looks like a simple ring here, this electron orbiting the proton nucleus forms a kind of three-dimensional standing wave. It's almost impossible to visualize, so we'll use a two-dimensional wave model to explore it.

A standing wave is also called a stationary wave. Its ends are fixed in place. To get an idea of what one looks like, take a look at the collection of waves below left:

Every wave shown is a standing wave. The simplest, or fundamental, wave is shown top left. The wave function of an electron is like a standing wave with its two ends fixed together, and the point where they connect is called a node. It's the one place on the wave model where the electron's energy can be fixed in place, or localized.  The red dots in the animation below are nodes in a standing wave. The top wave (left) is followed by six waves that are harmonic overtones of the fundamental wave. It takes energy to increase the number of oscillations in a wave.  If you taped one end of a string to a smooth floor and snapped the other end back and forth horizontally in your hand, close to the floor, you would notice you have to snap harder to add more oscillations in the string.

Higher harmonic frequencies represent higher average electron energy. Each node, where the wave is stationary, is where the electron's energy can be localized, or pinned down to an exact value. Between nodes the electron's energy is diffuse, somewhere in the electron cloud.

From Wave Functions to Orbitals

A real hydrogen atom is not nearly as simple as my simple electron shell diagram suggests. Its single electron has a multitude of three-dimensional orbital shapes available to it. The catch is that these orbitals are all energy-dependent. When the hydrogen atom is in its (lowest energy) ground state, its single electron will always take the closest possible energy orbital. This orbital is analogous to the simplest fundamental standing wave, with one node (at its ends), shown at the top, above left.

If you do some fancy math by plotting the square of all the local amplitudes this electron can take along the simplest fundamental standing wave, you get an electron cloud density distribution that looks like the red/white mist over a black background at the top left in the diagram below. Again, this is a simpler two-dimensional image of what is really a three-dimensional shape. The brighter the area, the more likely you are to find the electron. The hydrogen atom's lowest energy state orbital is spherically symmetrical with one node. It is called 1s, shown at the top left in the diagram below:

(en:User:FlorianMarquardt; Wikipedia)

The electron in this state is very close to the nucleus. This image corresponds to my simple diagram of a single energy shell, shell #1, or n=1 as it is usually called. The simple energy shell atomic model, drawn with rings showing available electron energy levels, is called a Bohr model, after Niels Bohr.

An electron orbiting a nucleus can absorb energy, and if the electron absorbs enough energy (a minimum "packet" amount), it will move up into a higher energy orbital. I've shown this earlier for an oxygen atom, but I could show it for hydrogen too, by drawing an additional outer electron shell, shell n=2, with the electron now occupying that outer shell. I could also show the hydrogen atom more realistically using the orbital imagery above. This kind of imagery is based on the quantum mechanical model of the atom. In the early 1900's, Erwin Schrodinger combined the equations for the wave behaviour of the electron with Louis de Broglie's equation for wave-particle duality to come up with a mathematical model for the distribution of electrons in an atom, the "fancy math" I mentioned. The electron cloud orbital images above are the result of those calculations.

This new model for the atom no longer tells us where the electron is but where it might be. Our energized electron may now take one of two possible new orbitals, 2s or 2p. They are analogous to a standing wave with two nodes, one in the middle and the other one where the ends connect. We can add even more energy to our single electron, enough to allow it to move up into an even higher energy orbital. Now it has a choice of three possible orbitals: 3s, 3p or 3d. These orbitals correspond to a standing wave with three nodes. I could draw this simply by adding a third outermost circle to my Bohr atom drawing, representing an electron shell even further away from the nucleus. The nodes in the standing waves are represented as circles in the Bohr model. Each one represents a specific allowed energy of an electron. However, as we move up in energy states, this simple ring-type picture becomes less and less accurate. The electron can now take complex routes as it moves about the nucleus. Sometimes it is furthest away from the nucleus in its new higher energy orbital but other times it may not be.

Electrons, because they are standing wave functions, must have energies that correspond to the nodes in a standing wave. They aren't allowed to take on energies between these nodes (the "no's in my earlier Bohr excited oxygen diagram).

Each atom has a particular set of wave functions. Larger atoms usually have slightly closer 1s orbital electrons than a hydrogen atom does. The closest electron is more strongly attracted to a more strongly positive nuclear charge (more protons in it), and that means it has just a bit less potential energy. The standing wave function of a 1s orbital in a larger atom will be just a bit longer (a slightly longer wavelength has less energy) than the one for hydrogen. All of the larger atom's other electrons will therefore have slightly different wave functions too. The nodes will be shifted just a bit farther apart. Additional electrons also complicate orbital distances because the electrons interact with each other, sometimes in complex ways. Atoms all have the same basic arrangement (and shapes) of energy orbitals- 1s, 2s, 2p and so on, but each orbital will have its own specific energy unique to each atom. The energy "rungs" are special to each atom.

If we go back to the excited hydrogen atom, even higher energy orbitals are possible. In fact, if enough energy is supplied to the electron in the hydrogen atom,  it will move up each successive energy orbital and eventually leave the highest possible energy orbital altogether, leaving the proton nucleus by itself. The atom in this state, where one or more electrons have left it, is called ionized. The hydrogen ion has a charge of +1, thanks to the lone proton that's left. It is completely ionized because it lost all of its electrons. An oxygen atom would have to lose all eight of its electrons to be completely ionized.

The Basic Idea Behind an Emission Spectrum

An atom in which one or more electrons have moved up into higher state orbitals is called an excited atom. In time, the atom will eventually return to its ground or lowest energy state as its electrons return to their lowest possible energy orbitals. Sometimes this takes a tiny fraction of a second. In other cases it can take minutes, depending on the particular atom and the orbital involved. In order to return to ground state, the electron has to shed its excess energy somehow. It does this by emitting a tiny packet of light. That packet, called a photon, carries a specific amount of energy off with it. It is exactly the same amount of energy as the difference in energy shells. When an excited electron in the oxygen atom returns to normal, for example, it takes three quarters of a second to emit a green photon, if it is excited enough. Then it emits a red photon, taking a whole two minutes to do so, below left:

These photon energies match the energies of the two excited shells involved. If we could look at a spectrum of this light, we would see two bright bands of colour - one red and one green.

Emission Spectrum of Hydrogen

As we saw earlier, there are many energy shells available to the electron in a hydrogen atom. Even this simple atom, as a whole, doesn't emit just one colour of light, but it doesn't emit a continuous spectrum of colours like a rainbow either. It emits a sequence of bright spectral lines, each one unique to a particular drop in electron orbital energy in hydrogen atoms. Each elemental atom emits its own line spectrum, called an emission spectrum. An excited electron can drop down one, two, three or more energy orbitals in one go, like a person sliding down a ladder, one, two or three rungs at a time.

Excited atoms don't just emit light in the visible range either. Our hydrogen atom emits photons in both the ultraviolet (UV) and infrared range as well as various visible colours. The entire electromagnetic (EM) spectrum is shown below right.

A photon is a quantum packet of electromagnetic radiation. It can range in energy from a gamma photon to a radio wave photon. The wavelengths of gamma photons are so short (a few trillionths of a metre) that most people call them rays instead. Likewise, radio photon wavelengths are so long (generally up to 10 metres) that we call them waves instead. As the photon's energy decreases, its wavelength increases and its frequency decreases.

The emission spectrum of the hydrogen atom (shown below) is a small sampler of the entire EM spectrum. This emission spectrum serves as a unique fingerprint for hydrogen atoms. An excited oxygen atom will have a different distinct emission spectrum. Don't worry about all the symbols at the top yet, but notice how small the visible range is compared to the whole spectrum (ignore the colours - they don't correspond to the visible spectrum). The hydrogen spectrum we can see is just a small fraction of all the possible emission photons from hydrogen atoms.

Emission Spectrum of a Hydrogen Atom

(OrangeDog; Wikipedia)

Each of the spectral lines you see above corresponds to one excited electron jump, returning down one or more energy levels. There are a lot of energy levels available to it, but there are forbidden areas or gaps where the electron cannot jump. These are the white spaces in between the lines (the spaces in between the standing wave "rungs") in the emission spectrum. The energy of electrons (and photons and other fundamental particles too) is quantized. It comes in discrete packets. Each jump corresponds to a photon of a particular wavelength (measured in nanometers, nm, billionths of a metre) being emitted. The wavelength can be calculated using a formula called the Rydberg formula. The quantized electron energy levels of the hydrogen atom give you a series of discrete spectral lines, rather than a whole rainbow of colours, when excited hydrogen returns to its ground state.

Now take a closer look at the top symbols. Looking from the top left, you can see Ly-alpha, Ba-alpha and Pa-alpha, and so on. These are series, or groups, of spectral lines: Lyman series, Balmer series and Paschen series. They are grouped according to the energy shells (average orbital energies) of the Bohr model:


This looks complicated but it isn't really. You'll notice lots of interesting energy trends in this diagram if you play with it a bit. For example, look at an electron jump from n = 6 to n = 1. This jump releases a 94 nm wavelength photon of energy. That's the shortest wavelength photon in the diagram. That means it's the highest energy photon, well into the UV range. There's a big difference in energy between an n = 6 orbital and an n = 1 orbital. If we tip things on their head, an electron would have to absorb the same energy as a 94 nm photon in order to jump up from n = 1 to n = 6. The atom would have to be struck by a fast moving particle or bombarded with extreme UV radiation. Now look at an electron jump from n = 2 up to n = 6. Much less energy is required here, equivalent to a 410 nm (visible violet) photon. The n = 2 electron is further from the nucleus. It's less attracted to it, which means it has more potential energy than an n = 1 electron does, so it's easier to push further up to n = 6 energy.

Most of these spectral line emissions are very faint and they can only be seen in the lab. There, a sample of pure hydrogen atoms is used, and it will contain atoms with electrons in various different excited states. A single electron in a single atom doesn't emit all the photons of all the series. A single electron will make just one or a few jumps to reach its ground state, emitting one to a few photons of EM radiation in the process, not all at once but one at a time.

Looking at the various wavelengths for electron single-shell jumps, there is also a trend: The electron needs much more energy to jump one shell up from the lowest shell closest to the nucleus (n = 1 to n = 2; 122 nm) than it does to jump from n=3 to n=4 (1875 nm), for example. It takes much more energy to pull the electron away when it's close to the nucleus, the attractive positive charge, than when it's farther away it. You are seeing Coulomb's inverse square law of charge interaction at work.

The Rydberg calculations are complex and only the relatively simple single electron emission of hydrogen atoms has been fully worked out. Spectra of atoms with just a few electrons have been worked out in some detail but it is much more difficult to do because electrons in each atom interact with each other, and that complicates the calculations.

You don't need to do any calculations to obtain a visible emission spectrum of any atom. You just need a pure source of the atoms, a way to excite them, and a prism called a spectroscope, to separate out the emitted photon wavelengths.

The Lyman series lines are all electron jumps down to the lowest energy shell. See how they all go down to n = 1? These emissions are all in the ultraviolet band of the electromagnetic spectrum, including a line at 122 nm wavelength, 103 nm wavelength and so on.

The Paschen series of hydrogen emission lines corresponds to electron jumps back down to the third energy shell. These lines are in the infrared range, from 820 nm to 1870 nm, so we can't see them either with the naked eye.

The Balmer series of spectral lines are jumps down to the second energy shell (the hydrogen is still in an excited state and the electron will eventually jump down to the n=1 lowest energy shell, emitting an invisible 122 nm UV photon in the process).

The Balmer emissions are mostly in the visible part of the spectrum, which means we can see most of them. The Balmer emission spectrum looks like this:

Emission Spectra Are Atom Footprints

There are actually six lines in the Balmer spectrum, above,  but you can only see four of them. The two invisible lines would be to the far left. They are just within the UV range, under 400 nm, so we can't see them. They represent electron energy shells n = 7 and n = 8. These two shells are farther out from the furthest shell (n = 6) shown in the emission series diagram earlier, and they represent two even higher energy states possible for the electron.

410 nm, 434 nm and 486 nm lines all fall into the visible violet/blue/green range and a far right line at 656 nm shows up as red to our eyes. In emission spectra, some lines are brighter than others. Red emission is especially strong from hydrogen atoms. It's a common electron jump. Click on this link to find out why. This colour alone, in fact, is used as a signature of hydrogen, the most common atom in the universe. It is what makes much of the Orion nebula, for example, appear reddish purple to us:

Hydrogen plasma glows the same reddish purple because its visible emission is in the Balmer series, mixing intense red with three fainter bluish tones, shown in the centre of the plasma tube below. Hydrogen atoms in the plasma state form a partially ionized gas containing hydrogen ions, electrons and neutral excited atoms. If you pass this light through a prism you will get the Balmer emission spectrum, shown above.

(Alchemist-hp (talk) (; Wikipedia)

Teachers can have fun with other atoms by performing a fairly simple flame test in the lab. When enough energy is applied to atoms (heat from a Bunsen burner for example), they glow with specific colours. Electrons are absorbing and releasing packets of energy according to their specific electron orbital energies. As they release energy, they release photons - they glow. Like hydrogen, each atom's colour is the combination of its visible emission spectrum lines (the wavelength energies of its electron jumps):

Emission Spectra Versus Absorption Spectra

A hydrogen atom must absorb the exact energy of a particular energy shell. This means it must absorb the energy equivalent to a particular wavelength photon in order to later emit it. Again this is because of the quantized packet nature of electrons (and photons). This means that hydrogen and other atoms give us absorption spectra that are the exact opposite of their emission spectra. The black lines in the absorption spectrum match the coloured lines in the emission spectrum below:

Emission Spectrum Of Oxygen

An atom with more electrons, such as oxygen, with eight electrons, emits a much more complex visible emission spectrum:

Notice an especially bright red line and green line in the spectrum above. They are common electron orbital shifts in this atom. The green colour is the colour of most Northern Lights displays. Less common red Northern Lights glow higher up in the atmosphere:

(this photo was taken from the International Space Station)

Up there, oxygen atoms are far enough apart that they have enough time to emit red photons before another atom strikes them and absorbs that energy. An oxygen atom's complete EM emission spectrum would contain hundreds of lines.

In Atoms Part 3, we'll continue to explore atoms and light, especially hydrogen. We focus next on the Sun, a massive ball of almost all hydrogen.

Wednesday, November 28, 2012

Atoms Part 3: Atoms And Heat

Incandescent light bulbs, stars, and hot briquettes on the barbecue, like the ones below, all glow brightly. The atoms in them emit light.


When atoms are very close together, they interact with each other, and when they do, they can sometimes emit light. In this case, the colour of the light they emit depends on their average energy. Some light bulbs, especially the old incandescent ones, as well as briquettes and stars glow brightly because they are hot.

From A Line Spectrum To A Continuous Spectrum

Hydrogen, the simplest atom there is, can emit dozens of different photon wavelengths when it is excited. That's a lot of lines in hydrogen's electromagnetic (EM) emission spectrum, as we saw in Atoms Part 2, but it is nowhere near a continuous EM spectrum. The visible emission spectrum of hydrogen is even simpler - it contains just four lines:

The sample of hydrogen that scientists use to obtain these spectra is very pure. A sample mixture of excited and ionized hydrogen gas containing both atoms and molecules would make the emission spectrum more complex. It would more vaguely resemble a full continuous spectrum like the one you see through a prism held up in sunlight. If we think about what the emission spectra of mixtures of atoms might be, say bound up in molecules, we start to wonder if we're going to approach a continuous emission spectrum, where all possible lines (wavelengths of emission photons) show up, and we do get closer to one. But even emission spectra of molecules resolve into distinct spectral lines, when you use a very good spectroscope. The Sun's emission spectrum is a continuous spectrum, which means there are no, even tiny, white gaps between spectral lines. The Sun's visible emission spectrum is a what you see when you put a sunbeam through a prism, or a rainbow:

Something else must be going on here, besides atoms and possibly a few molecules, emitting their emission spectra.


The Sun's Continuous Emission Spectrum

With what we've learned about emission spectra, you might expect to see something like a combination of hydrogen and perhaps helium emission line spectra superimposed on each other when you look at sunlight through a prism. And why shouldn't you? Our Sun is made of mostly hydrogen (71% of its mass; 91% of its atoms) and a little helium (27% of its mass; 8.7% of its atoms). But you don't. You see a continuous spectrum of visible colour rather than spectral lines. You would see a continuous spectrum even through a good spectroscope.

In this case, atoms emit light as they did before. But the spectrum they emit is different . . .

Black Body Radiation

If you looked at our Sun from outer space it would look like a glowing white sphere. Our atmosphere makes it look more yellow and it's a very common misconception that the Sun looks somewhat yellow from space:

(NASA image from International Space Station)

There is something very interesting about the Sun's white glow. It doesn't matter what the Sun is made of! It doesn't depend on the kinds of atoms involved. It could be a solid ball of iron and, if that iron ball were the same temperature as our Sun, it would glow the same white colour. Any other star at the same temperature as our Sun glows the same white colour, no matter what its composition is.

How can this possibly be true?

At the turn of the century, scientists didn't know much about electron orbitals in atoms. They didn't understand emission line spectra. They were focused instead on the colours of glowing hot objects. For example, Max Planck, looking at hot metals, wondered why any kind of metal, when it's heated, goes through the same sequence of glowing colours. It gets hot and begins to glow dim red. Then the red gets brighter and begins to shift to yellow, then to white, and finally to bluish-white. Why?

He realized that a hot object gives off light, or more precisely, EM radiation, known as thermal radiation. He also realized that as an object grows hotter, the intensity of the EM radiation increases as the wavelength decreases. The light it emits gets brighter as it gets hotter, and it shifts from longer wavelength red to shorter wavelength blue. Here is the relationship, based on experimental data, in graph form, below right:

The wavelength of the EM emission from the hot object is shown in micrometres (millionths of a metre) along the bottom of the graph. The intensity of the EM emission is plotted along the y-axis. At 300 K (around 27°C), the object emits only a few infrared photons. Notice how the blue line peaks at around 10 ยตm? We sense this wavelength of radiation as feeling warm to the touch. At around 1000 K (725°C; green line) the object is hot enough that it starts to glow dull red. At around 6000 K (red line; that's about how hot the surface of the Sun is) the object looks bright white. See how the red line peaks right at the visible spectrum? If you look at sunlight through a spectrum you see a nice continuous rainbow. This spectrum is called the Sun's black body spectrum. So what's a black body?

Black Body

Our Sun is a good, but not perfect, example of a black body. A perfect black body, in physics, is an object that absorbs all incoming EM radiation but doesn't reflect any back. A black charcoal briquette (below right) comes close to a perfect black body:

The briquette is opaque, unreflective (almost) and black. It absorbs all the (at least visible) photons that strike it. Its visible absorption spectrum is continuous. Its emission spectrum, on the other hand, would be black if it were perfectly cold. But nothing in the universe is perfectly cold. It emits at least a few infrared photons. We sense these photons as warmth. Infrared photons are invisible to us, so a perfect black body at room temperature would look perfectly black like the charcoal. If we heat the charcoal it will get hot. It will radiate more infrared photons.
As we heat it further it will start to glow dull red at around 1000 K, then yellow, white and eventually blue. Heated further still, over 10,000 K, it will radiate ultraviolet (UV) photons, but it will continue to radiate some blue photons too so it will still look blue to us. It won't turn invisible. And it will continue to radiate lots of infrared photons as well. In fact, it will radiate a whole continuous series of photon wavelengths, some of higher and lower wavelengths, but most will be UV photons at this temperature.

It seems really odd that the wavelength of these emission photons doesn't depend on the charcoal being made of carbon atoms. It only depends on how fast the carbon atoms are oscillating. More precisely, it depends on how fast charges are oscillating among the atoms. When thermal energy (heat) is applied, atoms oscillate faster and faster. The electrons in them are along for the ride. They oscillate too.

How Atoms Emit Black Body (Thermal) Radiation

Let's stop here a moment and examine the electron. The nuts and bolts of black body radiation really focuses on what the electrons are doing. Just as in excited atoms, it's the movement of electrons that creates light.

The electron is a quantum wave function. According to quantum mechanics, each electron is defined by four quantum numbers. We already know one number. It describes the energy of the electron. Other numbers describe its spin (electrons come in two spins - up and down), its angular momentum (this defines the shapes of its orbitals) and its magnetic moment. This last number tells us that electrons act like tiny quantum magnets. Electrons also have a negative charge. As the electrons oscillate along with their atoms, they set up tiny oscillating perpendicular electric and magnetic fields. These fields propagate, or move, as electromagnetic (EM) waves:

How fast an atom (and electrons) vibrates determines the oscillation (frequency) of the EM radiation it emits.

A real object contains atoms that are oscillating at a variety of frequencies. They have various amounts of kinetic energy. The temperature of the object reflects the average kinetic energy of its atoms. That average determines the general frequency of EM radiation it emits, what colour it glows when it's hot.

The emission spectrum of black body EM radiation reflects a whole variety of frequencies, or wavelengths, of photons, with a majority vibrating at some particular wavelength. The peak wavelength is the average energy of the atoms in the object. The overall average of thermal energies is what the thermometer reads. There are no forbidden photon wavelengths in black body radiation. Thermal radiation, and the black body spectrum of that radiation, depends only on the temperature of the object, not on its elemental make up.

Thermal radiation is yet another way that the electrons in atoms can emit light. The mechanism behind thermal EM radiation is subtly different from atomic EM emission, but in both cases, energized atoms release excess energy in the form of photons. When atoms are excited, the excess energy is localized in their electrons. When atoms gain thermal energy, the excess energy is distributed across the entire atom in the form of kinetic energy. It moves faster. Both mechanisms can and often do happen at the same time in one atom. Very hot materials are full of atoms that are both excited and thermally energized.

Why a Black Body is Assumed to Be a Solid Body

When we look at sunlight through a prism, we see a black body spectrum rather than an atomic emission spectrum. This has to do with how close the sun's atoms are. Thermal energy is atoms with kinetic energy. Thermal energy is what makes atoms jostle around amongst each other when they are close together in a solid. They can't go anywhere because they are chemically bound together, so they oscillate or vibrate instead. Pure elements in solid form melt when they get hot enough. If we take a ball of iron and heat it, it's going to glow red but its also going to melt. Molten iron glows the same red, then white, then blue. Some iron, if hot enough, will also vaporize into gaseous iron. In gases, atoms can move more freely. In this case, atoms, with their shells of electrons, act like tiny beach balls that bounce off each other. The electron shells have a spring-like quality - they deform a little like a spring, transferring thermal energy from atom to atom when they collide. A gas tends to expand when it is heated. The atoms in a (non-compressed) gas don't have much of a chance to set up oscillations. That is why scientists tend to focus on oscillations that set up thermal radiation in solid materials where atoms are forced to stay close together and vibrate.

Hmm, the Sun isn't solid is it? It is in a fourth kind of physical state called plasma. Plasma is a state that is physically similar to a gas but the Sun is so massive that its atoms, even though they contain a great deal of thermal energy, are forced to stay close together, close enough to set up thermal oscillations, because they are pushed down from the outside in by gravity. The Sun is surrounded by a cloud of gas, called a corona, made visible during a solar eclipse, below:

(Luc Viatour /;Wikipedia)

Like some planets, it has an atmosphere. Most of this gas consists of ionized and excited atoms. Gravity pushes atoms into the Sun but the energy from its nuclear fusion blows atoms away from it too. If we blocked out the hot Sun itself and looked at the spectrum of the gas around the Sun, we would see atomic emission line spectra of those gases.

How Do Hot Objects Cool Down?

In a hot object, energy is transferred from atom to atom and it is also radiated away as thermal radiation (heat and sometimes, light). Hot objects eventually cool down as their thermal energy is transferred to other atoms, such as those in the air or in other nearby objects, and as kinetic energy of atoms is converted into, and carried off as, EM radiation.  An atom all by itself can have kinetic energy, and that energy is reflected in the atom's velocity. But it isn't accurate to say an individual atom has thermal energy. The atom can't interact with other atoms, so it can't release its kinetic energy as thermal radiation. It can only release excess energy by emitting photons from its excited electrons. High up in the atmosphere where the thermosphere lies, atoms are very few and far between, but those that are present are continually bombarded by fast moving electrons and other particles streaming from the Sun and accelerated along Earth's magnetic field lines. These collisions excite the atmospheric atoms and transfer a lot of kinetic energy to them. That energy makes the thermosphere incredibly hot, up to 2000 C (calculated based on average velocity). But, if you placed a thermometer up there, it would read well below freezing because so few atoms would collide with the mercury inside it and transfer their kinetic (thermal) energy to it. Thermal energy is the energy of multiple atoms close enough to each other to conduct and transfer kinetic energy.

A Closer Look at the Sun's Spectrum

There are no perfect black bodies in real life, with one exception - black holes. They absorb all EM radiation. Their black body radiation is better described as Hawking radiation, as temperature depends on the mass of the black hole, and it is the subject my article on black holes.

Our Sun, however, is a pretty good approximation of a black body but it also contains excited hydrogen atoms, within its chromosphere and photosphere, two layers that are cool enough for these atoms to exist in excited, but not ionized, atomic form. Deeper inside the Sun, hydrogen atoms are fully ionized into seething plasma made of protons and free electrons. Excited hydrogen atoms are emitting line spectra that signal their presence but the Sun is a very hot object. Its intense black body radiation (its thermal radiation) overwhelms its atomic emission spectra. Discrete spectral emission lines can be carefully picked out from the Sun's black body emission spectrum, however, representing excited hydrogen atoms, hydrogen ions, a few helium atoms and ions, etc. The radiation from the Sun is a very complex mixture of not only excited atom and ion emissions but of intense thermal radiation as well as intense EM radiation from nuclear fusion as well as other processes. Its radiation covers the whole visible spectrum and much of the entire EM spectrum as well - as gamma rays, X-rays, UV rays, radio waves, etc., all emanate from it.  The Sun is a mess of radiation, reflecting an overall surface temperature (an average energy) of around 6000K. That is why it looks white.

The Sun's Line Emission and Absorption Spectra

Scientists have some tricks to get around the overwhelming black body radiation from the Sun in order to see its hydrogen emission spectrum. They can block out the Sun itself and examine its corona through a spectroscope. Or, they can look through a telescope with a hydrogen-alpha filter. This optical filter allows only a narrow range of light around the H-alpha wavelength (the bright red line emission in the Balmer emission spectrum). The Sun seen through this filter, you guessed it, looks like a giant red ball:


Scientists can do one even better by looking very carefully at the emission spectrum of the Sun. By doing so, they can make out hydrogen's absorption spectrum within the Sun's emission spectrum. They can make out many fine black lines in it, called Fraunhofer lines:

You need a very good prism to see them. Joseph von Fraunhofer himself was shocked to see these dark lines through a set of new improved prisms he had just made. He spent many years studying and measuring these lines. They show up exactly where the hydrogen gas emission lines do and they represent hydrogen's absorption spectrum embedded in the Sun's black body spectrum. It means that near the surface of the Sun, between it and our spectroscope, a modern version of Fraunhofer's prism, hydrogen atoms are cool enough to absorb EM radiation. They block out emission lines in the black body spectrum. If you look carefully at the spectrum above, however, you will notice that there are many more lines here than those that match the visual absorption spectrum for hydrogen. The Sun also contains some helium, a little bit of carbon and even very tiny amounts of iron and other heavy atoms. These elements also contribute Fraunhofer lines. If you read Atoms Part 1, you might be asking yourself how these heavy elements got into the Sun. It's a small star and it doesn't make them. 1.5% of the dust cloud that condensed into the Sun billions of years ago contained heavy elements. Much of that cloud was dust leftover after large ancient stars blew up at the end of their lifespans.

Scientists can look at stars and tells us how hot they are as well as what they are made of. If a star looks bluish-white, they know its temperature is around 8000K. If they look at it through a spectroscope, they will see a continuous spectrum, with a brightened blue region, and various absorption lines too, like the Fraunhofer lines. These lines are the absorption lines of atoms near the surface of the star; they tell scientists what the star's surface is made of.

Here is a black body applet to play with and get a feel for the concept:

Temperature versus Wavelength of Black Body Radiation

From Black Body Radiation To The Modern Quantum Mechanical Model Of The Atom

Planck understood black body radiation as a classical effect of heat applied to an object. He knew that when an object absorbs enough energy (heat) its atoms begin to vibrate. The relationship between the wavelength and the intensity of light emission from hot objects suggested to Planck that atoms vibrate like little harmonic oscillators, but how?

The Accidental Beginning of Quantum Mechanics

Before he could get very far, Planck saw a problem with his theory and it was a big one. He was working with classical electromagnetic theory to understand how atoms, when heated, act like harmonic oscillators. This sounds a little familiar so far doesn't it? The problem is that when he used Rayleigh-Jeans law, a classical law that's part of this theory, to calculate the relationship between the intensity and the wavelength of the objects' radiation, the solution didn't match his experimental results. According to this law, the number of electromagnetic vibrational modes is proportional to the square of the frequency. Each mode has the same energy so as the number of modes increases, energy increases. As the modes increase, wavelengths get shorter, and intensity approaches infinity:

This implies that a black body (at a high enough steady temperature) emits EM radiation of infinite intensity. Our Sun, at around 5000 K, would have grown infinitely bright. Naturally, it hasn't. Planck had to fix the problem and he did so by suggesting that EM radiation did not follow classical laws. Instead, EM radiation could only be emitted in discrete packets of energy that are directly proportional to the wavelength. Applying this adjustment brought the theoretical solution into line with the experimental results. For Planck it was a desperate shot in the dark, and at first he didn't know why it worked. He effectively reduced the number of electromagnetic modes possible. What at first seemed like an arbitrary fix, became an object of fascination to scientists at the time. Several physicists (Einstein, Heisenberg, Born, Bohr, de Broglie, Dirac, etc.), seeing a giant new possibility open up, took this work and expanded on it to create the modern quantum mechanical model of the atom, a giant breakthrough in our understanding of how atoms work. The energy of a photon is directly proportional to its wavelength. The intensity of the light from a hot object depends only on the number of photons coming from it, not on the energy of the photons. Intensity is delivered in discrete packets or quanta in other words. The reduced modes of electromagnetic vibration that Planck came up with are what we now call photons.


Over this article and the previous one, we took a close look at the emission and absorption spectra of hydrogen, as well the black body spectrum of an object almost entirely composed of hydrogen, in order to see how electron movement inside atoms works. It all boils down to two simple concepts:

First, electrons move away from the nucleus into higher energy orbitals when they absorb energy, and they release that energy by emitting light when they return to their lowest energy state.

Second, when an object gets hot, its atoms bounce against each other and oscillate, and the electrons in them vibrate. The electromagnetic vibration of electrons is what light is made of - a propagating electromagnetic oscillation.

The emission of light from countless sources around us owes itself to how electrons behave in atoms. By examining how atoms emit light, we followed in the footsteps of many physicists who devoted their lives to understand how the atom works: the modern quantum mechanical model of the atom.

Next we'll look at how atoms bond together in Atoms Part 4A - Atoms and Chemistry.

Tuesday, November 27, 2012

Atoms Part 4A: Atoms and Chemistry – Atomic Orbitals and Bonding

In Atoms Part 2 and Part 3, we explored how the electrons in atoms emit photons of electromagnetic radiation by comparing different kinds of spectra from hydrogen atoms and from the Sun, essentially a huge ball of hydrogen.

We're not done with electrons in atoms - not only do they change energy states by moving into different orbitals, they interact with electrons in other nearby atoms. In a nutshell, this is what chemistry is.

Chemistry is All About Bonds

You may have heard of two basic kinds of bonds: ionic and covalent.  We will explore and compare them in the next article. They both achieve the same goal: atoms bond with each other because they want to find the lowest possible energy state. Chemical bonding helps atoms achieve this goal. In order to understand bonding, we first need to look at the atoms themselves and how their electrons are configured, and that is what we're about to do here.


Orbitals: Their Shapes and Their Electrons

In atoms, electrons occupy orbitals. An orbital is a cloud-like area around the atom's nucleus where an electron is likely to be found. To give you an idea of what these shapes look like, the first five atomic orbital shapes are shown below.

From left to right they are the 1s, 2s, 2px, 2py and 2pz orbitals. The 2px, 2py and 2pz are actually suborbitals, subtypes of the 2p orbital. All this will become clearer as we go on.

Orbitals play a crucial role in how atoms bond with each other. There is an orbital rule every atom must obey - only two electrons can occupy the same orbital, and only if their spins are opposite. So, the 1s and 2s orbitals can fit two electrons in them, and the 2px, 2py and 2pz orbitals, likewise, each can only fit in two electrons.

This rule is based on the Pauli exclusion principle, which says that no two electrons in an atom can share all four of the same quantum numbers. Quantum numbers are part of the quantum mechanical model that describes the atom. These numbers describe the energy, angular momentum, magnetic moment and spin of electrons. The shape of each electron orbital depends on the electron's angular momentum. The energy of the electron determines which orbital it occupies. The electron's magnetic moment is behind all magnetic phenomena. That leaves spin, and electrons can choose one of two possible spins. This means that two, and only two, electrons can share the same orbital (or suborbital) because each electron can have one of two possible quantum spins. All the other quantum numbers of these two electrons will be the same.

You can quickly find out how many electrons any atom has by looking at the periodic table:
The number in each square is the atomic number. That's the number of electrons (and protons) in each atom. Hydrogen [H] has only one electron while chlorine [Cl] has 17 electrons, for example.

Hydrogen just has one (ground state) orbital, 1s1. The superscript "1" tells you the number of electrons occupying the orbital, in this case just one. Lithium [Li] has three electrons so it fills up the 1s orbital (this orbital can fit two electrons) and sets one electron in the next highest energy 2s shell: 1s22s1. Phosphorus [P] with 15 electrons is written as 1s22s22p63s23p3. Notice that the 2p shell allows six electrons in it, while the 3s orbital allows 2 electrons. Remember that the 2p orbital is actually made up of three suborbitals (take a quick look at the previous orbital diagram, at the three suborbitals to the right). Each of these three suborbitals holds two electrons, one of each spin. The suborbitals keep the electron pairs separate. A way to visualize the p orbital is shown below. Each p suborbital (a separate colour) has two lobes and it lines up along one of three axes:
This is what a typical p orbital looks like, whether it is 2p, 3p, 4p and so on. As the number in front increases, the p orbital's energy increases, so a 3p orbital has more energy than a 2p orbital, for example. The overall shape stays the same. The atomic nucleus is in the middle where the lobes intersect.

Now let's compare the p orbitals of two atoms. Argon [Ar], a noble gas atom, has 18 electrons (1s22s22p63s23p6). Its outermost 3p orbital is full; it has 6 electrons in it. Another atom, phosphorus has 15 electrons (1s22s22p63s23p3). It has a 3p orbital that's only half filled, with three electrons. Argon's filled orbitals make it very stable. The more stable an atoms is, the lower its potential energy is. This allows argon to exist in a very low energy state and it likes to stay that way. It is a very nonreactive, or inert, atom. The half-filled 3p orbital in phosphorus, on the other hand, makes its electron configuration a bit less stable. This atom is reactive; it can adopt a lower energy argon-like stability if it attracts three electrons to itself. It can do this by forming bonds. This is how atomic orbitals make chemistry possible.

The d orbital is higher energy yet. It can hold up to ten electrons. It holds a maximum of two (opposite spin) electrons in each of five suborbitals. This orbital looks a bit like a fancy three-dimensional daisy, shown bottom middle, below:

Electron Orbitals Versus Electron Shells

You have probably heard of electron shells and valence shells before. For example, argon, a noble gas, has a full valence shell of eight electrons.

Talking about orbitals and shells can get a bit confusing, so let's compare the two. If you look at a typical Bohr diagram of argon, shown below, you will see rings, or shells as they are called, representing specific energies at which electrons may be found.

(commons:User:Pumbaa (original work by commons:User:Greg Robson); Wikipedia)

The maximum number of electrons per shell depends on the shell. The first or closest shell can hold two electrons. The second one can hold eight, the third can hold 18, the fourth can hold 32, and so on. Inner shells generally must be filled before outer ones. The outermost shell of electrons is called the valence shell. Notice that argon has eight electrons in its third shell, which is its valence shell. At first glance it looks like argon's valence shell is less than half full. It has eight out of 18 possible electrons in it. Shells consist of subshells. Subshells and orbitals are the same thing. So, a p subshell is a p orbital (and remember the p orbital can be further divided into three suborbitals). The number in front of the subshell indicates what the electron energy is. A 3p subshell belongs to shell n = 3 in a Bohr diagram. Argon has eight n = 3 shell electrons. The three p suborbitals account for six electrons in total, so where do the other two come from? From the 3s orbital - it also has n = 3 energy, and being an s orbital, it contains two electrons when filled.

Argon has eight electrons in its valence shell (n = 3), which consists of two subshells or orbitals: 3s and 3p. The 3s (two electrons) and 3p (six electrons) subshells make up the n = 3 electron shell (eight electrons). As I said, the n = 3 shell can hold even more electrons – 18 in total. There is another orbital available to electrons with n = 3 energy: the d orbital. The 3d orbital can hold up to ten electrons in it. Take another quick look at the daisy-shaped d orbital diagram above. Argon has no electrons in this orbital. Its 3s and 3p orbitals, however, are full and that makes it stable.

Transition Metals: An Exception to the Orbital-Filling Scheme

There are a few exceptions to the general orbital filling scheme. One exception you might come across is the transition metal group. Many gems such as rubies and sapphires, owe their brilliant colours to the uniquely spaced electron orbitals of transition metal atoms inside them. It is also why transition metals can form a variety of different oxidation states. For example, Iron [Fe] can form both Fe2+ and Fe3+ ions when it reacts with oxygen to form iron (II) oxide and iron (III) oxide. Vanadium [V] has even more oxidation states – four, each with its own attractive colour in solution.

Nickel [Ni] is a transition metal atom with ten more electrons than argon. It does not just go ahead and fill up the 3d orbital, however. It fills up the 4s orbital first.

(commons:User:Pumbaa (original work by commons:User:Greg Robson); Wikipedia)

In transition metals, the inner 3d orbital generally has more energy than the valence shell 4s orbital.

Noble Gas Orbital Writing Shortcut

A shortcut to writing out long orbital notations is to use a noble gas core. Noble gases (group 18 on the periodic table) have completely filled orbitals. Our example argon is one of them. A shortcut for phosphorus, for example, uses the next smallest noble gas core. Phosphorus has 15 electrons, five of which are valence electrons, confined in two more orbitals of electrons than neon has. Neon [Ne], with 10 electrons, is written as 1s22s22p6, so for phosphorus we can write [Ne]3s23p3. Nickel, above, can be written as [Ar]4s2 3d8.

Halogens (group 17 on the periodic table) are just the opposite of the noble gases. They have an outer shell of seven electrons rather than the stable eight of the noble gases. These elements want just one more electron very badly and that makes them highly reactive. They gain this electron by reacting with other elements.

Fluorine [F], shown as a Bohr diagram below, is a great example.

It's the most reactive element there is. It will attack even inert materials like glass, and it will even form compounds with the heavier noble gases, which are generally nonreactive. Once fluorine bonds with something, that bond is so strong that almost nothing can break it. This makes Teflon so perfect as a non-stick non-reactive coating. It's made of carbon bonded with fluorine.

Now that we understand what makes some atoms more stable than other ones, we can explore how atoms increase their overall stability by bonding with each other, in Atoms Part 4B – Ionic and Covalent Bonds.