The wave function of an electron in the ground state of hydrogen atom
ψ=πa031e−r/a0 The probability density
ρ=4πr2∣ψ∣2=a034r2e−2r/a0
drdρ=a038r[1−a0r]e−2r/a0=0 So, the most probable value value of r
rmp=a0 The expectation value of r
<r^>=∫0∞rρdr=∫0∞a034r3e−2r/a0=23a0
Comments
Leave a comment