Question

An electron is moving on a circular path around a stationary neutron under gravitation interaction. Mass of the neutron and electron are $M$ and $m$ respectively. If Bohr’s quantum condition holds here the minimum permissible de Broglie wavelength associated with the electron will be

• A. $\frac{h^{2}}{2 \pi G M m}$
• B. $\frac{h^{2}}{2 \pi G M m^{2}}$
• C. $\frac{h^{2}}{2 \pi G M^{2} m}$
• D. $\frac{h^{2}}{4 \pi G M^{2} m}$

Answer 1

Answer: (B)

$\frac{m v^{2}}{r}=\frac{\textit{GMm}}{r^{2}}$
$mvr=\frac{n h}{2 \pi }$
$\lambda = \frac{h}{\text{mv}}$
$\lambda min = \frac{h^{2}}{2 \pi G M^{2} m}$