Finding Wavelength of Incident Radiation on H-Atom

[Saitama]

Homework Statement

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

Homework Equations

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 canceled out hc on both the sides but then got stuck. I don't understand what to do next?

 

[pmsrw3]

Use the Rydberg formula.

 

[Saitama]

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.

 

[Saitama]

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?

 

[Saitama]

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

Is it 4?

 

[Saitama]

I have found my answer, sorry for the disturbance.

 

[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.