Hydrogen's level holds states with ,

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch Radial functions, orbital size and Rydberg states

Problem

Hydrogen's

n = 4

level holds states with

l = 0

1

2

and

3

, all at one energy. Use the standard hydrogenic averages, with

a_0 = 0.052918\,\mathrm{nm}

and

e^2/4\pi\epsilon_0a_0 = 27.211\,\mathrm{eV}

. ((a)) Calculate

\langle r\rangle

for each of

4s

4p

4d

and

4f

in units of

a_0

, and give the largest and the smallest in nm. ((b)) Calculate

\langle 1/r\rangle

for each of the four states and use it to find the energy

E_4

in eV. ((c)) Explain in two or three sentences how four states of different size can share one energy.

Browse the problem library