Only certain emission lines show up in absorption spectrum

[eprparadox]

I'm reading Eisberg's Modern Physics and in it, in the atomic spectra chapter, he says:

"We have been discussing the emission spectrum of an atom. A closely related property is the absorption spectrum. This may be measured with apparatus similar to that shown in figure (5-1) except that a source emitting a continuous spectrum is used and a glass-walled cell, containing the monatomic gas to be investigated, is inserted somewhere between the source and the prism. After exposure and development, the photographic plate is found to be darkened everywhere except for a number of unexposed lines. These lines represent a set of discrete wavelength components which were missing from the otherwise continuous spectrum incident upon the prism, and which must have been absorbed by the atoms in the gas cell. It is observed that for every line in the absorption spectrum of an element there is a corresponding (same wavelength) line in its emission spectrum. However, the reverse is not true. Only certain emission lines show up in the absorption spectrum. For hydrogen gas, normally only lines corresponding to the Lyman series appear in the absorption spectrum; but ,when the gas is at very high temperatures, e.g. at the surface of a star, lines corresponding to the Balmer series are found. "

There's a few of questions that come to mind:

1. For an emission spectrum, let's say, for example, it takes 10 eV to get the gas molecule to go from the n = 1 state to the n = 4 state. If I bombard a gas molecule with 10 eV of energy, then does it make a direct transition to that n=4 state or does it (for however small amount of time) stop by the intermediary states?

2. Let's say it's now in this n = 4 state. What happens? I assume it'll try and find it's way back to the n = 1 state. But it'll go from n = 4 to n =3 and emit? And then n = 3 to n = 2 and then emit? And then to n = 1 and emit again?

3. Maybe answers to #1 and #2 above will help, but I didn't get why this had to be true: Only certain emission lines show up in the absorption spectrum.

Thanks so much

 

[mfb]

1. For an emission spectrum, let's say, for example, it takes 10 eV to get the gas molecule to go from the n = 1 state to the n = 4 state. If I bombard a gas molecule with 10 eV of energy, then does it make a direct transition to that n=4 state or does it (for however small amount of time) stop by the intermediary states?

It makes a direct transition.

2. Let's say it's now in this n = 4 state. What happens? I assume it'll try and find it's way back to the n = 1 state. But it'll go from n = 4 to n =3 and emit? And then n = 3 to n = 2 and then emit? And then to n = 1 and emit again?

That is possible, but a direct transition back is possible as well. It can also go from 4 to 2 to 1 or from 4 to 3 to 1.

Transitions from 4 to 3 will show up in the emission spectrum if the source is hot enough. To show up in the absorption spectrum you need a large amount of atoms in state 3 - something you'll rarely have in these setups.

 

[eprparadox]

Thanks for the response.

Why will the transition from 4 to 3 show up only if the source is hot enough. Is it because if it's not hot enough, there won't be enough states in the n = 4 energy level to begin with?

 

[mfb]

Why will the transition from 4 to 3 show up only if the source is hot enough. Is it because if it's not hot enough, there won't be enough states in the n = 4 energy level to begin with?

Right. On the other hand, cold hydrogen won't emit anything anyway, while it will still absorb something.

 

[Khashishi]

The emission lines do exist for every absorption line, but sometimes these lines are very weak and therefore don't show up in the spectrum. This is because the population of the upper state is low. You can estimate the population using Boltzmann statistics. Higher energy states will barely be populated at lower temperatures.

2. Let's say it's now in this n = 4 state. What happens? I assume it'll try and find it's way back to the n = 1 state. But it'll go from n = 4 to n =3 and emit? And then n = 3 to n = 2 and then emit? And then to n = 1 and emit again?

They will all happen with some probability. There is a branching factor for each transition. Typically, the 4 to 1 transition has higher probability than the 4 to 2 or 4 to 3 transitions, if it is allowed by selection rules.