Find wavelength

[Pranav-Arora]

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?

[pmsrw3]

Use the Rydberg formula.

[Pranav-Arora]

Use the Rydberg formula.

How can i use the Rydberg formula here?

[pmsrw3]

How can i use the Rydberg formula here?
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.

[Pranav-Arora]

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?


I get three different wavelengths.

[pmsrw3]

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

[Pranav-Arora]

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

Is it 4?

[Pranav-Arora]

I have found my answer, sorry for the disturbance. :smile:

[brocq_18]

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.

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

Thanks

[pmsrw3]

A side question here, If I have an atom that is not hydrogenic, how do I find this wavelength?
It's very, very hard. Like quantum mechanics and supercomputers hard.