Finding Wavelength of Incident Radiation on H-Atom

In summary, the conversation discusses the incident of monochromatic radiation on a hydrogen atom in the ground state. The atom absorbs energy and subsequently emits six different wavelengths of radiation. The Rydberg formula is suggested to determine the wavelengths emitted by the atom. It is clarified that the atom does not emit all six wavelengths at once, but rather in a specific order depending on its energy state. It is also mentioned that finding the wavelengths for atoms other than hydrogen is extremely difficult.
  • #1
Saitama
4,243
93

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


[tex]\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}[/tex]
I canceled out hc on both the sides but then got stuck. I don't understand what to do next?
 
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  • #2
Use the Rydberg formula.
 
  • #3
pmsrw3 said:
Use the Rydberg formula.

How can i use the Rydberg formula here?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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?
 
  • #7
pmsrw3 said:
Right. So, what state would the H atom have to go into to subsequently emit 6 different wavelengths?

Is it 4?
 
  • #8
I have found my answer, sorry for the disturbance. :smile:
 
  • #9
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.
 

1. What is the purpose of finding the wavelength of incident radiation on a hydrogen atom?

The purpose of finding the wavelength of incident radiation on a hydrogen atom is to understand the energy levels and transitions of the electron in the atom. This information is crucial in understanding the behavior of atoms and molecules, and is used in various fields such as spectroscopy and quantum mechanics.

2. How is the wavelength of incident radiation on a hydrogen atom determined?

The wavelength of incident radiation on a hydrogen atom can be determined using the Rydberg formula, which relates the wavelength to the energy levels of the atom. The formula is: 1/λ = R (1/n12 - 1/n22), where R is the Rydberg constant and n1 and n2 are the initial and final energy levels, respectively.

3. What is the significance of the Balmer series in finding the wavelength of incident radiation on a hydrogen atom?

The Balmer series is a specific set of spectral lines that are produced when the electron in a hydrogen atom transitions from higher energy levels to the second energy level. These lines correspond to specific wavelengths of light, and are used in the calculation of the wavelength of incident radiation on a hydrogen atom.

4. Can the wavelength of incident radiation on a hydrogen atom be measured experimentally?

Yes, the wavelength of incident radiation on a hydrogen atom can be measured experimentally using techniques such as spectroscopy. In spectroscopy, light is passed through a sample of hydrogen gas and the resulting spectrum is analyzed to determine the wavelengths of light that are absorbed or emitted by the sample.

5. How does the wavelength of incident radiation on a hydrogen atom vary with the energy level of the electron?

The wavelength of incident radiation on a hydrogen atom is inversely proportional to the energy level of the electron. This means that as the energy level of the electron increases, the wavelength of the incident radiation decreases. This relationship is described by the Rydberg formula, which shows that the energy levels and wavelengths are directly related.

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