A small particle of mass m moves in such a way that the potential energy U = `ar^(2)` where a is a constant and r is the distance of the particle from the origin. Assuming Bohr's model of quantization of angular momentum and circular orbits, find the radius of `n^(th)` allowed orbit.

Options

A. `n^2`
B. `n`
C. `sqrtn`
D. `1/(sqrtn)`

Answer

C

Explanation

`-1/2 xx P.E.= K.E`
`=-1/2 (- 1/2 mkr^2) = 1/2 mv^2 , mvr = (nh)/(2pi),`
`v^2 = (n^2 h^2)/(4pi^2 m^2 r^2) ,r^4 = (n^2 h^2)/(2pi^2 m^2 k) ` or `r^00 sqrtn`