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no of wavelengths during excitation Watch

1. 1. The problem statement, all variables and given/known data
hi
i came across this problem on an aqa physics a past question.

How many different wavelengths of electromagnetic radiation can be emitted after
atomic hydrogen is excited to level 4?

2. Relevant equations

3. The attempt at a solution
i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
i calculated in this manner for level 3 to the ground, 2 to the ground state etc.

can someone someone clarify where i am going wrong?
thanks
2. the answer (6) implies ground state is n=1
so there are 3 gaps:
______________ 4

______________ 3

______________ 2

______________ 1

and so 6.
3. (Original post by aurao2003)
1. The problem statement, all variables and given/known data
hi
i came across this problem on an aqa physics a past question.

How many different wavelengths of electromagnetic radiation can be emitted after
atomic hydrogen is excited to level 4?

2. Relevant equations

3. The attempt at a solution
i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
i calculated in this manner for level 3 to the ground, 2 to the ground state etc.

can someone someone clarify where i am going wrong?
thanks
If the hydrogen is in n = 4, then the possible ways it can return to the ground state are:
4 --> 3 --> 2 --> 1
4 --> 3 --> 1
4 --> 2 --> 1
4 --> 1

Radiation is emitted when each of these transitions between levels occurs, and the wavelength of the radiation is related to the energy difference between the levels n and m by:

So the number of different wavelengths of radiation we can get is the same as the number of distinct transitions, which is 6:
4 --> 3
4 --> 2
4 --> 1
3 --> 2
3 --> 1
2 --> 1
4. thanks a million!

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