For a hypothetical hydrogen like atom, the potential energy of the system is given by `U(r)=(-Ke^(2))/(r^(3))`, where r is the distance between the two particles. If Bohr's model of quantization of angular momentum is applicable then velocity of particle is given by:

Options

A. `v = (n^(2)h^(3))/(ke^(2) 8 pi^(3) m^(2))`
B. `v = (n^(3)h^(3))/(8ke^(2) pi^(3) m^(2))`
C. `v = (n^(3)h^(3))/(24ke^(2) pi^(3) m^(2))`
D. `v = (n^(2)h^(3))/(ke^(2) 8 pi^(3) m^(22))`

Answer

C

Explanation

`(d[U(r)])/(dr) = (3Ke^(2))/(r^(4)) rArr ` Magnitude of the force
`therefore (3Ke^(2))/(r^(4)) = (mv^(2))/(r)` and we know mvr `(nh)/(2pi) or r (nh)/(2pi mv)`
` 3ke^(2) xx (8 pi m^(3) v^(2))/(n^(3)h^(3)) = mv^(2), v = (n^(3)h^(3))/(24 Ke^(2) pi m^(2))`