Calculate Longest & Shortest Wavelength?

  • #1
Electrons accelerated by a potential difference of 13.14 V pass through a gas of hydrogen atoms at room temperature.

A) Calculate the wavelength of light emitted with the longest possible wavelength.

B) Calculate the wavelength of light emitted with the shortest possible wavelength.

I've solved part B, but cannot solve part A. Any suggestions?

Part B [CORRECT]
V=13.14V so KE=13.14 eV

En=-13.6/(n^2)
E1= -13.6 eV

E= -13.6 eV + 13.14 eV
E= -0.45 eV

E2= -3.4 eV
E3= -1.5 eV
E4= -0.85 eV
E5= -0.544 eV
E6= -0.378 eV

E=E5-E1
E=(-0.544)-(-13.6)
E= 13.056eV * 1.6e-19 J
E= 2.089e-18 J

E=hc/λ
λ=hc/E
λ=(6.626e-34)*(3e8)/(2.089e-18)
λ= 9.52e-8 m


Attempt at Part A) [INCORRECT]

Longest wavelength is in Paschen series (n=3)
E=E4-E3
E=(-0.85)-(-1.5)
E= 0.65eV * 1.6e-19 J
E= 1.04e-19 J

E=hc/λ
λ=hc/E
λ=(6.626e-34)*(3e8)/(1.04e-19)
λ= 1.91e-6 m
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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The Paschen Lyman and Balmer series are not the only ones available.
Anyway, why choose E4-E3, why not E9-E8 ... isn't that a longer wavelength?
What about the energy lost getting to E9 or E4 or whatever?

The shortest wavelength emmitted corrsponds to the maximum amount of energy lost .... that would be a transition from E (the electron energy) to E0 (the lowest hydrogen energy level).

This you know.

By the same argument:
The longest wavelength emmitted corresponds to the _______ amount of energy lost .... that would be a transition from E (the electron energy) to E__ (the ________ hydrogen energy level).

Fill in the gaps.

------------------------------

note: this assumes the electron gets captured in one go via an electric dipole interaction ... there are other ways to get radiation out of that setup: i.e. Bremsstrahlung
 
Last edited:

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