The 6 hydrogen spectral line series'

[horseb0x]

I noticed that the hydrogen spectral lines are grouped into 6 series and given a value for n. I also noticed that each series was named after its discoverer but "coincidentally?" falls into a specific region of the EM spectrum so the Lyman series (n=1) of lines are all in the UV region, the Balmer series (n=2) in the visible region, the Paschen series (n=3) the IR region etc. Firstly is this "n" the principle quantum number? If so what have these series' got to do with the different energy shells of the Bohr model? For example what has the balmer series got to do with the 2nd energy shell? Finally what is it about this correlation that causes the lines of each series to appear where they do. For example why do the lines all appear in the UV region when n=1 but lie in the visible region when n=2?

 

[kevinalm]

In general, the principal quantum number n indicates the depth of the electrostatic potential well, n=1 being 'nearest' to the nucleus and therefor at the lowest potential energy. Higher numbers are at a higher potential. This is a major trend among all elements with an occasional exception in some of the higher Z atoms, iirc. Now, emission occurs when an electron jumps from one level to another (lower) level and the various series are named for the end state number n.

Since n=1 is the lowest an electron can 'fall' into the energy well, it is not surprising that the transitions ending in n=1 are the most energetic.

Edit: I should probably also mention that as n goes to high numbers, the difference in energy between levels becomes smaller, approaching a finite limit such that the n=infinity to n=1 transition is equal to the ionization energy, around 13 ev for hydrogen if memory serves.

 

[James R]

I noticed that the hydrogen spectral lines are grouped into 6 series and given a value for n. I also noticed that each series was named after its discoverer but "coincidentally?" falls into a specific region of the EM spectrum so the Lyman series (n=1) of lines are all in the UV region, the Balmer series (n=2) in the visible region, the Paschen series (n=3) the IR region etc. Firstly is this "n" the principle quantum number?

Yes. For example, the Balmer series of spectral lines is the group of transitions that end up with the atom in the n=2 state. So, it includes transitions from n=3 to n=2, n=4 to n=2, n=5 to n=2, ... n=infinity to n=2.

For example why do the lines all appear in the UV region when n=1 but lie in the visible region when n=2?

Most likely, they do not. (I'd have to check to be sure.) While the Lyman and Balmer and Paschen series do not overlap, I'm fairly sure the Paschen series does overlap with the Pfund series (n=4). All subsequent series overlap to some extent.

 

[kevinalm]

You're right, there is indeed considerably more overlap than I thought.

http://en.wikipedia.org/wiki/Hydrogen_spectral_series

 

[eclectician]

Yes. For example, the Balmer series of spectral lines is the group of transitions that end up with the atom in the n=2 state. So, it includes transitions from n=3 to n=2, n=4 to n=2, n=5 to n=2, ... n=infinity to n=2.



Most likely, they do not. (I'd have to check to be sure.) While the Lyman and Balmer and Paschen series do not overlap, I'm fairly sure the Paschen series does overlap with the Pfund series (n=4). All subsequent series overlap to some extent.

However: There is a limit to the number "n" in the Balmer series. It cannot go to infinity because that would result in a wave of zero frequency. Right?

 

[D H]

However: There is a limit to the number "n" in the Balmer series. It cannot go to infinity because that would result in a wave of zero frequency. Right?

Wrong. The underlying equation is the Rydberg formula,

$$\frac 1 {\lambda} = R_{\infty}\left(\frac 1 {m^2} - \frac 1 {n^2}\right)$$

Here R[sub]∞[/sub] is the Rydberg constant, m and n are integers with n>m. m=1 represents the Lyman series, m=2 the Balmer series, and so on. For any given series, As n goes to infinity the wavelength approaches a limit given by m[sup]2[/sup]/R[sub]∞[/sub].