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 8 pi^3 m^2)`
C. `v= (n^3 h^3)/(Ke^2 8 pi^3 m^2)`
D. `v= (n^2 h^3)/(24Ke^2 8 pi^3 m^2)`

Answer

C

Explanation

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