Question

Suppose potential energy between electron n proton at distance "r" is given by... (-ke^2)/(3.R^3)...Use bohr's theory to obtain energy levels of such hypothetical atom

Answer 1

Since H atom is a bounded system U cannot be positive
U = - ke2/3r3
Electrostatic force of attraction at a distance r will be
F = -dU/dr
  = -ke2/r4
Assuming a circular radius of the orbit
mv2/r = ke2/r4
=> mv2 = ke2/r3
=> ½mv2 = ke2/2r3
=> KE = ke2/2r3
E = KE + U
  = ke2/2r3 + (- ke2/3r3)
  =  ke2/6r3
Gives the energy level of the atom

Answer 2

Answer:

n^h^6/384m^3k^2e^4pi^6