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.

No comments:

Post a Comment

Note: Only a member of this blog may post a comment.