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Q.

A small particle of mass m moves in such a way that PE $= - \frac{1}{2} m k r^{2}$ ,where k is a constant and r is the distance of the particle from origin. Assuming Bohr's model of
quantization of angular moment and circular orbit, r is directly proportional to:

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a

n²

b

n

c

$\sqrt{n}$

d

n³

answer is C.

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Detailed Solution

$\begin{array}{l} - \frac{1}{2} \times PE = KE \\ = - \frac{1}{2} [- \frac{1}{2} m k r^{2}] = \frac{1}{2} m v^{2}, m v r = \frac{n h}{2 π} \\ v^{2} = \frac{n^{2} h^{2}}{4 π^{2} m^{2} r^{2}}; r^{4} = \frac{n^{2} h^{2}}{2 π^{2} m^{2} k^{2}} \\ r \propto \sqrt{n} \end{array}$

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