Nuclear & Particle Physics - Hydrogen Spectrum

In the hydrogen spectrum, the ratio of the wavelength for Lyman-radiation  (n = 2  to  n = 1) to Balmer-radiation (n = 3  to  n = 2)  is

A. 5/48
B. 5/27
C. 1/3
D. 3
E. 27/5

(GR0177 #21)

Solution:

Rydberg formula:



λ_vac = the wavelength of the light emitted in vacuum
R_H = Rydberg constant for Hydrogen
n₁ and n₂ are integers such that

For Lyman-radiation (n = 2 → n = 1):



For Balmer-radiation (n = 3 → n = 2):



The Ratio:



Answer: B