Finding Wavelength of Incident Radiation on H-Atom

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Discussion Overview

The discussion revolves around determining the wavelength of incident radiation on a hydrogen atom in its ground state, which absorbs energy and subsequently emits radiation of six different wavelengths. The context includes theoretical aspects of atomic transitions and the application of the Rydberg formula.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes using the Rydberg formula to find the wavelengths associated with the hydrogen atom's transitions.
  • Another participant questions how to apply the Rydberg formula in this context, suggesting that the emitted wavelengths are determined by this formula.
  • A participant clarifies that the question may imply that many hydrogen atoms are illuminated, leading to the emission of six different wavelengths, rather than a single atom emitting all six.
  • There is a discussion about the number of different wavelengths emitted by an H atom transitioning from the n=3 state to n=1, with one participant stating they find three different wavelengths.
  • Another participant inquires about the state necessary for an H atom to emit six different wavelengths, suggesting n=4 as a possible answer.
  • A participant expresses that they have found their answer and apologizes for any disturbance caused.
  • A side question is raised regarding how to find the wavelength for non-hydrogenic atoms, with a response indicating that it is a complex problem requiring advanced methods.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of the Rydberg formula for hydrogen but do not reach a consensus on the specific state required for the emission of six wavelengths or the clarity of the original question.

Contextual Notes

The discussion includes assumptions about the nature of atomic transitions and the clarity of the problem statement, which remains unresolved.

Saitama
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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?
 
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Use the Rydberg formula.
 
pmsrw3 said:
Use the Rydberg formula.

How can i use the Rydberg formula here?
 
Pranav-Arora said:
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.
 
pmsrw3 said:
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.
 
Pranav-Arora said:
I get three different wavelengths.
Right. So, what state would the H atom have to go into to subsequently emit 6 different wavelengths?
 
pmsrw3 said:
Right. So, what state would the H atom have to go into to subsequently emit 6 different wavelengths?

Is it 4?
 
I have found my answer, sorry for the disturbance. :smile:
 
pmsrw3 said:
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
 
  • #10
brocq_18 said:
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.
 

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