Difference in atomic energies 2p 1s for hygrogen and duterium

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Homework Help Overview

The discussion revolves around calculating the difference in wavelength between the 2p→1s transition in ordinary hydrogen and deuterium, focusing on the underlying atomic energy differences due to the reduced mass variations between the two isotopes.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between wavelength and frequency, questioning the validity of the initial equation presented. They consider the implications of the reduced mass difference on energy levels and seek clarity on the specific energy differences between the 2p and 1s states.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made in deriving energy levels and the specific differences between the 2p and 1s states in individual atoms. Some guidance has been offered regarding the relevance of reduced mass, but clarity on the energy differences remains to be fully addressed.

Contextual Notes

Participants are navigating the complexities of atomic structure and energy level calculations, with a focus on the differences introduced by isotopic variations. There is an acknowledgment of assumptions in the energy derivation process that may need further examination.

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Homework Statement


Calculate the difference in
wavelength between the 2p→1s line in ordinary hydrogen and in deuterium (which has a nucleus containing
a proton and a neutron).

Homework Equations



the difference in wavelength is related with the difference in frequences with the relationship :
c=(Δλ) (Δf) but Δf =hbar/ΔE so Δλ= c ΔΕ / hbar ,so what's the difference in energies between 2p and 1s ?

The Attempt at a Solution

 
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helpcometk said:

Homework Statement


Calculate the difference in
wavelength between the 2p→1s line in ordinary hydrogen and in deuterium (which has a nucleus containing
a proton and a neutron).

Homework Equations



the difference in wavelength is related with the difference in frequences with the relationship :
c=(Δλ) (Δf) but Δf =hbar/ΔE so Δλ= c ΔΕ / hbar ,so what's the difference in energies between 2p and 1s ?

The Attempt at a Solution

c = (Δλ) (Δf) can't be right. If Δf = 0, you'd have Δλ = 0, and c clearly doesn't equal 0.

Think about why the energies would be different in the two atoms. What's the primary difference between ordinary hydrogen and deuterium? Why would this affect the energy levels? Think about the assumptions that went into deriving the formula for the energy of a state.
 
That was the first part of the formal question actually and I've hidden it becuase in knew the answer, there is reduced mass differnce between deuterium and Hydrogen.
But what can't understand is the difference between 2p and 1s in an individual atom
 
Hmm, I have to admit I'm confused at to what exactly you're getting stuck on. Can you be more specific?
 
Is 2p state correspondin to n=2 and 1s to n=1 ?
 
Yes.
 
Thanks
 

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