A small particle of mass m move in such a way the potential energy `U = (1)/(2) m^(2) omega^(2) r^(2)` when 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 , show that radius of the nth allowed orbit is proportional to in

Explanation

To show that the radius of the nth allowed orbit is proportional to the square root of n, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Potential Energy**:
The potential energy \( U \) of the particle is given by:
\[
U = \frac{1}{2} m \omega^2 r^2
...