Question

A smallparticle of mass m moves in such a way that P.E. = –$\frac{1}{2}$mkr², 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 –

• A. n²
• B. n
• C. $\sqrt{n}$
• D. None of these

Answer 1

Answer: (C)

$\sqrt{n}$

Answer 2

–$\frac{1}{2}$× P.E. = K.E.

= –$\frac{1}{2}$ [–$\frac{1}{2}$mkr²] = $\frac{1}{2}$mv², mvr = $\frac{nh}{2\pi}$

v² = $\frac{n^{2}h^{2}}{4\pi^{2}m^{2}r^{2}}$; r⁴ = $\frac{n^{2}h^{2}}{2\pi^{2}m^{2}k^{2}}$