# Find wavelength

1. Jul 31, 2011

### Saitama

1. The problem statement, all variables and given/known data
Monochromatic radiation of specific wavelength is incident on H-atom in ground state. H-atom absorbs energy and emit subsequently radiations of six different wavelength. Find wavelength of the incident radiation.
(a)9.75 nm
(b)50 nm
(c)85.5 nm
(d)97.25

2. Relevant equations

3. The attempt at a solution
$$\frac{hc}{\lambda}=\frac{hc}{\lambda_1}+\frac{hc}{\lambda_2}+\frac{hc}{\lambda_3}+\frac{hc}{\lambda_4}+\frac{hc}{\lambda_5}+\frac{hc}{\lambda_6}$$
I cancelled out hc on both the sides but then got stuck. I don't understand what to do next?

2. Jul 31, 2011

### pmsrw3

Use the Rydberg formula.

3. Jul 31, 2011

### Saitama

How can i use the Rydberg formula here?

4. Jul 31, 2011

### pmsrw3

Well, it's an H atom, right? So the wavelengths it can absorb and the wavelengths it can emit are determined by the Rydberg formula.

Suppose I gave you an H atom in the n=3 state. How many different wavelengths could it emit on its way back to n=1?

By the way, I think the original question is a little unclear. I don't think it is intended to imply that a SINGLE H atom emits six different wavelengths. I think what is meant is that if you illuminate a lot of H atoms with the incident wavelength (or illuminate one atom many many times) and look at everything that comes out, you will see six different wavelengths.

5. Jul 31, 2011

### Saitama

I get three different wavelengths.

6. Jul 31, 2011

### pmsrw3

Right. So, what state would the H atom have to go into to subsequently emit 6 different wavelengths?

7. Jul 31, 2011

### Saitama

Is it 4?

8. Jul 31, 2011

### Saitama

I have found my answer, sorry for the disturbance.

9. Aug 2, 2011

### brocq_18

A side question here, If I have an atom that is not hydrogenic, how do I find this wavelength?

Thanks

10. Aug 2, 2011

### pmsrw3

It's very, very hard. Like quantum mechanics and supercomputers hard.

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