# Spectra in the Classroom

Every chemical element has a unique `signature' which can be revealed by analyzing the light it gives off. This is done by spreading the light out into a spectrum -- basically, a rainbow.

It may seem remarkable that we can learn about the composition of distant stars by studying the light they emit. In fact, we can learn a great deal, not only about the chemical elements present, but also about physical conditions. The key is to spread the light out by color, producing a spectrum like the one shown here. This class explores some of the basic ideas used to analyze spectra.

## Atoms and Photons

The nature of matter was debated for thousands of years. Suppose you have a chunk of gold, for example, and you start cutting it into smaller and smaller pieces. Can you always cut any piece, even a very small one, into two smaller pieces of gold? Or is there some minimum size a piece of gold can have? We know the answer -- the smallest possible piece contains just one atom of gold. Atoms are the building blocks of matter. There are about one hundred different kinds of atoms in the universe -- these are known as the chemical elements.

The nature of light posed a very similar question: Is light composed of waves or of particles? If light is waves, then one can always reduce the amount of light by making the waves weaker, while if light is particles, there's a minimum amount of light you can have -- a single `particle' of light. In 1905, Einstein found the answer: light is both! In some situations it behaves like waves, while in others it behaves like particles. This may seem strange and mystical, but it describes the nature of light very well.

### Wavelength and Energy. I

A wave of light has a wavelength, defined as the distance from one crest of the wave to the next, and written using the symbol λ . The wavelengths of visible light are quite small: between 400 nm and 650 nm, where 1 nm = 10-9 m is a `nanometer' -- one billionth of a meter. Red light has long wavelengths, while blue light has short wavelengths.

A particle of light, known as a photon, has an energy E. The energy of a single photon of visible light is tiny, barely enough to disturb one atom; we use units of `electron-volts', abbreviated as eV, to measure the energy of photons. Photons of red light have low energies, while photons of blue light have high energies.

### Wavelength and Energy. II

The relationship between energy E and wavelength λ is one of the most basic equations of quantum physics:

 λ = h c E .

Here c is the speed of light, and h is known as Planck's constant. Both c and h are constants of nature; they never change. From our point of view, the significance of this equation is that energy E and wavelength λ are inversely proportional to each other, and the relationship between them is the same here on Earth and in the most distant stars and galaxies.

## Signatures of the Elements

As quantum physics developed, physicists began to understand another puzzle. The light given off by atoms in a hot dilute gas does not form a spectrum of all colors; instead, only some colors are present, and each element produces a unique pattern.

 Hydrogen: a simple atom with a simple spectrum. Helium: slightly more complex than hydrogen, with one yellow line and a number in the blue. Neon: a very large number of lines in the red give neon signs their distinctive pink colors, but notice the two green lines. Argon: the pastel color of argon is due to a wide range of lines throughout the spectrum. Mercury: the strongest line, at 546 nm, gives mercury a greenish color.

### Atomic Transitions

Why do hot atoms behave this way? The answer involves two key ideas: first, each atom contains one or more electrons orbiting a central nucleus; second, in atoms of any given element, only certain orbits are allowed, and a very specific amount of energy is involved when an electron jumps from one orbit to another.

 We can illustrate this for hydrogen, which has only one electron. The allowed orbits of an electron in a hydrogen atom can be numbered using the symbol n, with n = 1 for the orbit closest to the nucleus, n = 2 for the next one out, and so on.

For orbit n, the smallest amount of energy required to completely separate the electron from the nucleus is

 En = 13.6  eV n2 .

### Energy Levels

This quantity En is the energy level of orbit n. For example, an electron in orbit n = 2 requires energy E2 = 3.4 eV to be separated from the nucleus, while an electron in orbit n = 3 requires only E3 = 1.51 eV; thus, orbit n = 3 is less tightly bound to the nucleus than orbit n = 2. When an electron jumps down from orbit n = 3 to orbit n = 2, it gives off energy E = E2 - E3 = 1.89 eV. This is exactly the energy of the photons which make up the red line of hydrogen. Likewise, electrons jumping from orbit n = 4 to orbit n = 2 produce the blue-green line, and electrons jumping from orbit n = 5 to orbit n = 2 produce the deep blue line. When an electron jumps from a high-numbered orbit to a low-numbered orbit, the atom emits a photon.

What happens when an electron in a hydrogen atom jumps up to a higher orbit? This takes energy, which has to come from somewhere. One way to supply the energy is with a photon, but the photon has to have exactly the right amount of energy -- no more, and no less. For example, an electron in orbit n = 2 can jump up to orbit n = 3 if it absorbs a photon with energy E = E2 - E3 = 1.89 eV.

### Emission and Absorption

Similar processes of emission and absorption happen in atoms of other elements. For atoms with more than one electron, the physics becomes much more complex, but the basic idea that electrons have only certain allowed orbits still holds. Each element has a different set of allowed orbits, so each element emits or absorbs photons with different energies -- and therefore, different wavelengths.

Molecules also produce spectral lines, but their spectra are much more complex than the spectra of single atoms, and typically show broad bands instead of narrow lines, as seen here.

 A spectrum of air. The bright bands are due to molecular oxygen (O2), molecular nitrogen (N2), and other molecules.

## Types of Spectra

Examining different kinds of light with a spectroscope reveals a wide variety of spectra. The appearance of a spectrum tells us something about the physical conditions which produce the light.

 Continuous spectrum: a smooth gradation of color, with no distinct features. Emission spectrum: bright lines on dark background. Absorption spectrum: dark lines superimposed on a continuous spectrum (shown in black & white because the subtle dark lines are hard to reproduce in color).

### Continuous Spectrum

For example, a continuous spectrum is a featureless rainbow of color. This kind of spectrum is the hallmark of `black-body' radiation (so-called because a black object, heated until it glows, emits this kind of light). A hot solid, liquid, or very dense gas produces a continuous spectrum; while a wide range of wavelengths are always present, the overall color of the light depends on the temperature. For example, a bar of iron heated in a fire glows dull red; if heated more it glows orange, and if heated well beyond its melting point it shines with a brilliant blue-white light.

 Continuous spectrum: a smooth gradation of color, with no distinct features.

### Emission Spectrum

In contrast, an emission spectrum consists of bright lines or bands on a dark background. Emission spectra are produced when atoms of a dilute gas are `excited' -- in effect, heated -- by an electrical current, ultraviolet radiation, or some other source of energy. Excited atoms have electrons in high orbits, and these emit photons with specific wavelengths when they jump back down to lower orbits (as explained above). Neon signs produce emission spectra; so do objects like the Lagoon Nebula (M8) and the Ring Nebula (M57).

 Emission spectrum: bright lines on dark background.

### Absorption Spectrum

Finally, an absorption spectrum, like the spectrum of sunlight shown here, consists of dark lines or bands on top of a continuous spectrum. Absorption spectra are produced when light from a hot object travels through a cooler, dilute gas. When a photon with exactly the right wavelength encounters an atom of the cool gas, it is absorbed and its energy used to kick an electron into a higher orbit; if enough atoms of gas are present, all the photons of that wavelengths are absorbed, while photons with other wavelengths get through. The atmospheres of stars produce absorption spectra.

 Absorption spectrum: dark lines superimposed on a continuous spectrum (shown in black & white because the subtle dark lines are hard to reproduce in color).

An element produces bright and dark lines with the same wavelengths. For example, hydrogen has three prominent lines with wavelengths of 434 nm, 486 nm, and 656 nm; these appear dark if the hydrogen is absorbing light, and bright if it is emitting light, but the same three wavelengths are seen in either case.

## REVIEW QUESTIONS

• What is the energy level E6 for an electron in a hydrogen atom with orbit n = 6, and how much energy is given off if this electron jumps to orbit n = 2?

• What kind of light does a hydrogen atom give off when an electron jumps from an orbit with n > 1 down to orbit n = 1? Is this light visible, or invisible?