Answer to Question #249810 in Physics for SRI

Question

The wave function of the hydrogen atom in its ground state (1s) is

ψ=(πa03)−12exp⁡(−ra0 where 

a0=0.529×10−8 cm. The charge density is

ρ(x,y,z)=−e|ψ|2, according to the statistical interpretation of the wave function.

Then the value of ⟨r⟩

⟨r⟩ is given by

a) 5a02

b) 2a02

c) 4a02

 d) 3a02

Answer 1

Answer: d)

$$⟨r^2⟩=3a_0^2$$