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

[helpcometk]

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

 

[vela]

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.

 

[helpcometk]

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

 

[vela]

Hmm, I have to admit I'm confused at to what exactly you're getting stuck on. Can you be more specific?

 

[helpcometk]

Is 2p state correspondin to n=2 and 1s to n=1 ?

 

[vela]

Yes.

 

[helpcometk]

Thanks