Spectral Line

The studies on sunlight (white light) showed that it consists of multiple colors, a spectrum of colors.

Dark lines cross the normal spectrum. (in comparison with the nearby bright regions). This lines represent wavelengths where there is less radiation than at nearby wavelengths.

Graphs of intensity vs. wavelength show narrow dips superimposed on the continuum.

Absorption and Emission Lines:

Kirchhoff noticed that when a beam of white light was passed through a gas tube, the spectrum showed dark lines. The gas was absorbing energy in a few specific narrow wavelength bands. This lines are known as absorption lines.

When the white light was removed, the spectrum showed bright lines, or emission lines, the wavelengths where absorption lines had previously appeared.

The gas emits or absorbs energy only in certain wavelength bands.

Kirchhoff found that the wavelengths of the emission or absorption lines depend only on the type of gas that is used. Each element or compound has it own set of special wavelengths. If two elements which don’t react chemically are mixed, the spectrum shows the lines of both elements.

Thus, the emission or absorption spectrum of an element identifies that element as uniquely as fingerprints identify a person.

Properities:

Absorption or emission depends in part on whether or not there is a strong enough background source providing energy to be absorbed.
The strength of the spectral lines depends on:

1) gas quantity

2) gas temperature

It worthmentioning that spectral lines has something to do with the classification of stars into spectral types.

The origin of spectral lines:

The processes that result in atoms being able to emit or absorb radiation at certain wavelengths are tied to the nature of matter and light.

The modern picture of the atom begins with the experiments of Ernest Rutherford, who studied the scattering of alpha particles (helium nuclei) off gold atoms:

Most of the alpha particles passed through the gold atoms without being deflected, suggesting that most of the atom is empty space!
Some alpha particles were deflected through large angles, suggesting a concentration of positive charge at the center of each atom. This concentration is called the nucleus. A sufficient number of electrons orbit the nucleus to keep the atom electrically neutral.

There were still some problems with this picture:

It did not explain why electron orbits were stable. Classical electricity and magnetism tells us that an accelerating charge gives off radiation. An electron going in a circular orbit is accelerating, since its direction of motion is always changing. Therefore, as the electrons orbit, they should give off radiation, lose energy and spiral into the nucleus. This is obviously not happening.
The second problem concerns the origin of spectral lines. There is nothing in the Rutherford model of the atom that allows for spectral lines.

The arrangement of spectral lines in a particular element is not random. For example Balmer formula.

Formation of spectral lines:

The first point to realize is that in a star the issue is not about the radiation from a single hydrogen atom, but from a large number of them.

There is a strong Hα absorption line in stars because many photons are removed from the continuum by this process. It is clear, however, that having a lot of hydrogen does not assure to have a strong Hα absorption. In order for such absorption to take place, a significant number of atoms must be in level 2, ready to absorb a photon. If all the hydrogen is in level 1, the Balmer series will not be seen, no matter how much hydrogen is present.

1) Excitation

Knowing the temperature in the atmosphere of a star, helps in using the Boltzmann equation to predict how many atoms will be in each state, i, and predict the strengths of various spectral lines.

2) Ionization

Intensities of spectral lines:

At low temperatures, essentially all of hydrogen is neutral, and most of it is in the ground state. Since little H will be in the second state, there will be few chances for Hα absorption. The Hα line will be weak.

As it heads to moderate temperatures, most of the hydrogen is still neutral. However, more of the hydrogen is in excited states, meaning that a reasonable amount will be in level 2. Hα absorption is possible. As the temperature increases, the Hα absorption becomes stronger.

At very high temperatures, the hydrogen becomes ionized. Since there is less neutral hydrogen, the Hα line becomes weaker. This explains why the Hα line is strongest in middle-temperature stars, and why the original scheme of classifying by hydrogen line strengths did not produce a sequence ordered in temperature.

For other elements the details will differ because of different energy level structures and different ionization energies. It should be noted that, after hydrogen and helium, the abundances of the elements fall off drastically. In fact, astronomers often refer to hydrogen, helium and ‘everything else’. The ‘everything else’ are collectively called metals, even though many of the elements don’t fit the common definition of a metal.

We now look at the properties of different spectral types, in order of increasing temperature.

In astrophysics it is generally to refer to the wavelength in air, since that is how it be measured at a telescope. The wavelength in air is that in vacuum divided by the index of refraction of air, 1.000 29.

The calculations of Balmer helped in chrystalization of Bohr atom.