A small particle of mass ‘m’ moves in such a way that its potential energy, 21P.E. = mkr2 ,where ‘k’ is a constant and ‘r’ is the distance of the particle from origin. Assuming Bohr’s model ofquantization of angular momentum and circular orbit, ‘r’ is directly proportion to

The potential energy of the particle is given by PE = mkr^2. According to Bohr's model of quantization of angular momentum, the angular momentum (L) is quantized and given by L = nħ, where n is the principal quantum number and ħ is the reduced Planck's constant.

The centripetal force required for the particle to move in a circular orbit is provided by the force due to the potential energy. This gives us:

m*v^2/r = d(PE)/dr

Differentiating PE with respect to r, we get:

d(PE)/dr = 2mkr

Substituting this in the above equation, we get:

m*v^2/r = 2mkr

Solving this equation for r, we get:

r = v^2/2k

According to Bohr's model, the velocity v of the particle is given by v = nħ/mr. Substituting this in the above equation, we get:

r = (n^2 * ħ^2) / (2mk)

So, the distance 'r' of the particle from the origin is directly proportional to the square of the principal quantum number 'n'.