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I think what you seems to have done is nC2.
Since I don't have the answer to this question, I cannot say whether it's correct or not. But according to me, the answer given by you is not correct since the question is asking for unique wavelengths in the sample.
here, you can see that total no. of wavelengths possible is 4 (4-1)/2 = 6. hence the formula is correct. I cannot xplain but I think you can see from the figure that as n increases, no. of wavelengths increases by n-1 because e has now n-1 more choices to dexcite
But all the electrons have been excited to nth energy state. Then how did in the rest of the transitions, except for the first one, the transitions have not started from nth enery level. Can you please explain???
Well, I rated you and accepted your answer but didn't realize about the present doubt. Anyways, can you please answer???
basically..
the correctest (a nu word )...xplaination is this
..
had it been a single hydrogen atom ...the no. of unique lines wud be .??? !!! ONLY ONE ..
but as there are many atoms of hydrogen ...so there are repetitions ...
but as a viewer ..one wud see ..nc2 types of lines ..(.all unique ) ..
these lines wud be comin from different atoms...
but make it clear ..that a single atom wud be giving a single line however.
But don't you think that you have also considered the repetitions.
See, suppose there are n Hydrogen atoms. In each one of them, the electron has been excited to the nth energy level. Now to come to the ground state, it can make various types of transitions. Lets say first it comes from n to n-1, then to some other energy level. But Besides this electron, there are n-1 other electrons that are also making transitions. So, don't you think that the transitions described by you will repeat.
Please answer.
@Nugorama
For a single H-atom, there are n-1 unique wavelengths, not ONLY ONE.
The question asks us to find the maximum number of unique wavelengths that this sample can emit.
And regarding this, for a single H-atom, the transitions have to be from n to n-1 to n-2 to n-3 to ...........n=1. So, in all, we have n-1 unique wavelengths.
You are confused between the number of transitions.
Here the question does not say that the number of transitions have to be one. It is not necessary that it has to reach the ground state in just one jump. But it just asks that what are the maximum number of unique wavelengths it can emit???
There was a question before the question that I have given here which asked us to find the no. of unique wavelengths for one H-atom. And its answer was n-1. The solution is also given.
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n(n-1)/2 . [not sure]