Spectral line formula [closed]

Two years back my friend told me a simple formula for calculating the number of spectral lines. But, now I'm a bit confused about it number of lines is =$\frac{2(n-1)}{2}$ is this right or is there any error in it?

closed as unclear what you're asking by user10851, CuriousOne, Gert, Ryan Unger, DanuMar 18 '16 at 10:25

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• minus infinity for the name – Jimmy360 Apr 9 '15 at 4:01
• sorry! however can you help me out with the formula, like if hydrogen atom is excited to 4th level, it can either go from 4 to 3, 2, 1 or 3 to 2,1 or 2,1 which then adds up to 6 lines(lights that's emitted), – curiouslearner Apr 9 '15 at 4:14

You can derive it simply by noting that each level can have $n-1$ transitions,so we have $n-1+n-2+...+1=n(n-1)/2$

Proof time:

Each level can have $n-1$ transitions

This gives us $S = n-1 + n-2 + n-3+...+1$

Lets take $S$ and do this:

$S = n-1 + n-2 + n-3+...+1$

$+S = 1 + 2 + 3 +...+ n-1$

$= n(n-1)/2$

(because there are as we can tell from $S = 1 + 2 + 3 +...+ n-1$, there are $n-1$ elements in the series)

QED

Let us not ignore the fact that there will be some overlaps too. For example, when there's a jump from 10 to 22 and a jump from 11 to 55, the spectral lines will overlap because 1/(10*10)-1/(22*22)=1/(11*11)-1/(55*55). Hence the actual number of spectral lines will be less than or equal to n*(n-1)*(1/2).

• This answer seems to be wrong. – Gonenc Jul 11 '15 at 16:46

If a electron in hydrogen jumps from $n_1$ to $n_2$ then number of spectral lines is given by formula: $$\frac{(n_1-n_2)(n_1-n_2+1)}{2}$$

• You might want to add an explanation of how that was arrived, simply stating the equation isn't particularly useful. – Kyle Kanos Jan 13 '16 at 15:07