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

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) (h2/2 π G M m) (B) (h2/2 π G M m2) (C) (h2/2 π G M2 m) (D) (h2/4 π G M2 m)

Tardigrade Admin · Accepted Answer

(m v2/r)=( textitGMm/r2) mvr=(n h/2 π ) λ = (h/ textmv) λ min = (h2/2 π G M2 m)

Q. 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

$\frac{h ^{2}}{2 π GM m}$

$\frac{h ^{2}}{2 π GM m ^{2}}$

$\frac{h ^{2}}{2 π G M ^{2} m}$

$\frac{h ^{2}}{4 π G M ^{2} m}$

$\frac{m v ^{2}}{r} = \frac{GMm}{r ^{2}}$
$m v r = \frac{nh}{2 π}$
$λ = \frac{h}{mv}$
$λmin = \frac{h ^{2}}{2 π G M ^{2} m}$

Q. 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

2πGMmh2​

2πGMm2h2​

2πGM2mh2​

4πGM2mh2​