Hydrogen Emission Spectrum

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Homework Statement


What wavelengths emitted from a hydrogen gas discharge tube are associated with transitions from higher levels down to the n = 1 level?
[a] infrared
visible
[c] mixture of infrared and visible
[d] ultraviolet



Homework Equations


Equations:
1/λ = Rh[1/(m^2)-1/(n^2)] Rh = 1.09 x 10^7 m^-1.



The Attempt at a Solution


Can someone explain hydrogen gas electron transition to me? This stuff is a little over my head.

I obtained various wavelengths with arbitrary quantum numbers greater than 1. I took +infinity as a bound since higher quantum numbers reaches the series limit.
1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(infinity)]
λ (+infinity ,1)= 91.6 nm

1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(4^2)]
λ (4 ,1)= 4.86 nm

The level transitions yield a photon with wavelengths corresponding to UV light.

I’m confused though because taking bounds of the 1.01 type down to 1 allows the photon to be associated with different lights. Do I have to keep m and n whole when doing this problem? With m & n being non-integral values n can be taken arbitrarily closer and closer to 1 (with n>1) pushing the wavelength to positive infinity. Non-integral values possess a different number of points in a dimensional space corresponding to different emissions.
 

Answers and Replies

  • #2
Dick
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Homework Statement


What wavelengths emitted from a hydrogen gas discharge tube are associated with transitions from higher levels down to the n = 1 level?
[a] infrared
visible
[c] mixture of infrared and visible
[d] ultraviolet



Homework Equations


Equations:
1/λ = Rh[1/(m^2)-1/(n^2)] Rh = 1.09 x 10^7 m^-1.



The Attempt at a Solution


Can someone explain hydrogen gas electron transition to me? This stuff is a little over my head.

I obtained various wavelengths with arbitrary quantum numbers greater than 1. I took +infinity as a bound since higher quantum numbers reaches the series limit.
1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(infinity)]
λ (+infinity ,1)= 91.6 nm

1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(4^2)]
λ (4 ,1)= 4.86 nm

The level transitions yield a photon with wavelengths corresponding to UV light.

I’m confused though because taking bounds of the 1.01 type down to 1 allows the photon to be associated with different lights. Do I have to keep m and n whole when doing this problem? With m & n being non-integral values n can be taken arbitrarily closer and closer to 1 (with n>1) pushing the wavelength to positive infinity. Non-integral values possess a different number of points in a dimensional space corresponding to different emissions.


Yes, you have to keep m and n whole numbers. That's quantization. There are only discrete states for bound electrons.
 
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Okay I understand this now. Thanks a lot!!
 

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