A small particle of massm 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.

A small particle of massm moves in such a way that the potential energ

1.	A small particle of massm 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.
Answer» `n^2` `n` `sqrtn` `1/(sqrtn)` SOLUTION :`-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`