For a one-electron system with a fixed nucleus of charge , Bohr's model gives and

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

For a one-electron system with a fixed nucleus of charge

Ze

, Bohr's model gives

r_n = n^2a_0/Z

and

E_n = -13.6\,Z^2\ \mathrm{eV}/n^2

, with

a_0 = 0.0529

nm. Use

hc = 1240

eV nm. Compare the three one-electron systems H (

Z = 1

), He

^+

(

Z = 2

) and Li

^{2+}

(

Z = 3

). ((a)) Give the ground-state radius

r_1

of each, in nm. ((b)) Give the ground-state energy

E_1

of each, in eV. ((c)) Give the wavelength of the

n_2 = 3 \to n_1 = 2

line of each, in nm.