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.

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