Atoms

127-134

In order to understand what starlight is "trying to tell us" we will need to understand some very basic ideas of atomic structure and how light interacts with atoms.

What is an Atom?

Atoms are mostly empty space! Figure 6.1 shows a video clip of what we think a hydrogen atom might look like. Most of the atom's mass (99.95%) is contained in a tiny dot called the nucleus and situated at the center of the atom. The volume of the nucleus is only 1 part in 1015 (one thousand-trillionth!) the volume of the atom. Surrounding the nucleus - at very precise locations is a scintillating "cloud". This is an attempt to visualize one of the strange ideas of quantum mechanics - the electron around the atom does not orbit (like a mini-solar system) but has an assignable probability of existing - for a fleeting instant - at a particular position. This scintillating pattern is sometime referred to as an electron cloud.

 

Main Ideas About Atoms

  • 3-Basic Particles: Atoms are made up of electrons (negatively charged) that exist outside the nucleus with neutrons (neutral) and protons (positively charged) particles within the nucleus. The mass of the proton and neutron are almost the same (neutron slightly more massive) and the electron is only about 1/2000th the mass of the proton.
  • Neutral Atoms have an equal number of protons and electrons giving a net charge of 0.
  • Ions are atoms that have either lost or gained an electron and hence are now charged. A negative ion is an atom that that has gained an electron, a positive ion is one that has lost an electron.
  • Isotopes are atoms that have the same number of electrons and protons but different number of neutrons. Isotopes are very similar to each other in chemical behaviour but can be quite different in other ways. Carbon 14, for example is a radioactive isotope of normal carbon.
Figure 6.1 Video clip showing what a hydrogen atom might look like.
  • Elements are atoms that have a specific number of protons and electrons. For example Carbon 12, Carbon 13 and Carbon 14 are all considered the same element - Carbon. They are isotopes of carbon.
  • Molecules are made up of atoms. For example water is a combination of 2 hydrogen atoms and 1 oxygen atom (hence H2O)
  • Energy Levels are the specific locations (radii) at which electrons can be found in an atom. The science of quantum mechanics gives very precise rules which govern the location of these energy levels.
  • Energy Quantization: Electrons can have only specific and strictly defined energy when in an atom. THis also governs how atoms can either absorb or emit energy.

Just How Does an Atom Produce Light?

In order to understand how atoms produce light it is important to recall the idea of the photon introduced in the last chapter. One of the great discoveries of the early 20th century was made by Max Planck and Albert Einstein. Energy is exchanged by atoms in complete units called quanta (hence the name Quantum Theory) and the way in which quanta are exchanged is the photon! An atom gains or loses energy by either absorbing or emitting a photon.

Figure 6.2 shows a simple version of the Hydrogen atom with the two lowest energy levels drawn. The letter "n" is used to indicate the principal quantum number which is one of the most fundamental ideas in quantum mechanics. Electrons can only exist in an atom if they are in one of these quantum levels. As an analogy, consider living in an apartment - you can live on the ground floor ("n = 1 level") or the 100th floor ("n = 100 level) but you can't live on the 21/3 floor for example. In this figure the electron is in the n= 1 or ground state.

Because the electron and proton attract each other we say that the electron is bound to the nucleus. The energy that binds the electron in an atom is called the binding energy and the only way that an electron can move in an atom is to either lose or gain precise amounts of energy that correspond to the binding energy of a specific energy level. The entire secret of stellar spectra is found here!
Figure 6.2 Energy levels in an atom refer to the possible locations at which electrons can be found.  

Now Planck's radical idea comes on the scene. Normally, electrons try to stay in the lowest energy level open to them. BUT - if the right flavor of photon happens by they get EXCITED! The atom can absorb the photon because it has exactly the right energy to move the electron to one of its higher energy levels. An atom in which one or more electrons are in levels above the lowest possible ones is said to be in an excited state.

 

The key point here is that the atom can only absorb discrete amounts of energy and this must exactly match the energies represented by the energy levels in the atom.

Now, suppose the atom is excited - then what? Usually after an extremely short period time the electron drops back down to a lower energy level. When this happens it re-emits a photon of the same energy as the energy difference between its starting and resting levels but now traveling in a random direction. Figure 6.3 illustrates this. A blue photon is just the right
flavour" for the atom - it is absorbed and then quickly re-emitted as another blue photon.

 
Figure 6.3 Flash animation showing how an atom responds to a photon of the "correct" frequency.

 

 

The Light - Energy Connection

There is a very convenient way to measure the energy of a photon of light. As we already know, the shorter the wavelength or (equivalently) the higher the frequency, the greater the energy of the light wave. Now that we are using the photon idea we can express energy of a photon in the following way:

Energy Photon = (Planck's Constant) X (Frequency of the Light)

or

E = hf

We can now give Planck's quantization idea a bit more detail. According to quantum physics energy is exchanged in strict accordance with the expression:

E = nhf

so, if we are receiving energy from a light source of frequency "f" we can only receive energy in packages of size: hf, 2hf, 3hf .... and so on.

(as a curious aside, the above formula combines both particle (photon) and wave (frequency) ideas! welcome to the strange world of quantum effects)
How do we use the light - energy connection? We can now talk about atomic transitions and the photons either given off or absorbed in terms of energy exchanges. This will be very useful when we begin to discuss how light is actually being produced by an astronomical phenomenon.

How to Excite an Atom

 
  • whisper sweet nothings in its ear! (not very effective)
  • feed it the right photons
  • collide with other atoms - the atom can sometimes absorb the right amount of energy to promote one of its electrons to an excited level
The last two techniques are the most common.

Continuum Radiation

The continuous "ROYGBIV" produced by an incandescent object provides an example of continuum radiation. Every wavelength is present from blue to deep red. (in principle - all wavelengths are present but the amount of light emitted drops rapidly as you move either direction away from the visible spectrum).

Discrete Radiation

This is the type of light produced by individual atoms. Un -able to radiate at just any wavelength (equivalently: any color, equivalently: any energy) the atom produces a discrete set of colors. We will look at Hydrogen gas in just a moment.

How to Make a Spectrum

A spectrum will, in general be a combination of both discrete and continuous processes. A star surface for example, will have individual atoms producing a myriad of discrete "lines" while the electrons present in the gas will produce a background continuum.

How Light Interacts With Matter

Now the pieces are starting to come together. Imagine heating a gas to a high temperature. Electrons will be liberated (ionization) and the atoms will begin to jostle, get excited and radiate their characteristic colors. Under this scenario we would be seeing a bright line spectrum. That is, a spectrum dominated by bright emission lines from atoms present in the gas. This is illustrated in the following:

If, on the other hand we shine continuous light through a cool gas, the atoms in the gas will selectively filter out specific frequencies - in fact the same frequencies - and dark lines will appear. This is called a dark line spectrum.

Our previous points about continuous, bright line (or emission) and dark line (or absorption) spectra are summarized in Kirchhoff's Laws:

Law 1: Hot objects (solid, liquid or gas) emit a continuous spectrum

 

Law 2: When a continuous spectrum passes through a cool gas, that gas will absorb discrete wavelengths corresponding to the transition energies of its constituent atoms. The result will be dark lines impressed on the spectrum.

 
Law 3: A heated gas will emit a discrete set of bright lines of exactly the same wavelengths as those absorbed by the gas when cool.
Figure 6.4 Gustav Kirchhoff Table 6.1 Kirchhoff's Laws

 

A Case Study: Hydrogen and Its Spectrum

Hydrogen is the simplest atom and produces the simplest spectrum. By our good fortune it also makes up over 70% of the mass of the universe! So ... understanding the Hydrogen spectrum is very important.

The following diagram is called an energy level diagram. We could have continued drawing concentric circles representing energy levels for an electron in a Hydrogen atom. More efficient, however, is this "flattened out" diagram that concentrates on the different energy levels and the transitions that can occur.

Figure 6.5 Energy level diagram for atomic hydrogen

 

The Hydrogen Atom Applet

If your computer has a Java plugin loaded then you may wish to run the following applet. This applet will illustrate the absorption and emission of electrons from a Hydrogen atom.

(Click on image to launch applet)

 
  Figure 6.6 Hydrogen atom applet

How Molecules Interact with Light to Help Create Spectral Windows

We are now able to understand better how spectral windows are formed in the atmosphere. Molecules are far less "picky eaters" compared to simple atoms. This is because molecules have many more allowable energy levels than atoms and can absorb photons over very large ranges of wavelength in the electromagnetic spectrum.

The applet shown in Figure 6.7 will allow you to investigate how one specific molecule (a chlorofluorocarbon molecule) absorbs over the EM spectrum. Other molecules like molecular nitrogen, molecular oxygen, water and carbon dioxide absorb in different parts of the spectrum. Collectively they produce the spectral windows that we saw in Chapter 5.1.

To use this applet first check the show CFC box shown on the bottom right. Photons will then, at random move across the screen. Some will be absorbed by the molecule if they are of the correct frequency.

  
  Figure 6.7 Applet that illustrates how a "CFC" molecule can absorb photons over a very large range in the electromagnetic spectrum. (Courtesy of The King's Centre for Visualization in Science)

 

 


To understand the structure of atoms and molecules and how these interact with light

Chp7.1,2