A hydrogen atom emits the line for which the electron falls from the level to the level

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Origins of quantum theory

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Line spectra, the Bohr atom and the old quantum theory

Problem

A hydrogen atom emits the line for which the electron falls from the level

n_2 = 5

to the level

n_1 = 3

. Take the Rydberg constant to be

R_H = 1.097\times10^7\ \mathrm{m^{-1}}

and treat the nucleus as fixed (no reduced-mass correction). ((a)) Find the wavelength of this hydrogen line, in nm. ((b)) Singly ionised helium, He

^+

, is a one-electron ion of nuclear charge

Z = 2

. Find the wavelength of its

5 \to 3

line, in nm.