Question

. Find the average distan e between the ele tron and proton in the Hydrogen ground-state. Use: hri = ˆ[infinity] 0 dr rP(r) where ϕ(r) = Ae−r/aB is the ground-state solution of the radial S hrodinger equation for the Hydrogen atom (aB is Bohr's radius), and P(r) = 4πr2 |ϕ(r)| 2 is the probability density that the ele tron would be lo ated in the spheri al shell between r and r + dr. First normalize the wavefun tion to obtain the onstant A: ˆ[infinity] 0 dr P(r) = 1

Answer 1

As data is given in the problem statement is below

ϕ(r) = Ae−r/aB

P(r) = 4πr2 |ϕ(r)| 2

r=0

After normalizing the distance between electron and proton will be 200 nm