Answer to Question #74411 in Atomic and Nuclear Physics for Deepesh Tripathi

Question

The ratio of areas within the electron orbits for the first excited state to the ground state for the hydrogen atom is

Answer 1

Radius of the nth orbit is given as
rn = (h2ϵ0/πme2) n2
For the ground state, n=1
For excited state, n=2
r2 = (h2ϵ0/πme2) n2
r1 = (h2ϵ0/πme2) n2
r2 / r1 = (h2ϵ0/πme2) n22 / (h2ϵ0/πme2) n12
r2 / r1 = n22 / n12
r2 / r1 = 22 / 12
r2 / r1 = 4 / 1
So the ratio between radii of the first orbital and the ground state radii is 4 / 1.