First slide

Bohr's atom model

Question

If potential energy between a proton and an electron is given $| U | = k e^{2} / 2 R^{3}$ , where e is the charge of electron and R is the radius of atom, then radius of Bohr's orbit is given by (h = Planck's constant , k = constant)

Moderate

A

$\frac{k e^{2} m}{h^{2}}$
B

$\frac{6 π^{2}}{n^{2}} \frac{k e^{2} m}{h^{2}}$
C

$\frac{2 π}{n} \frac{k e^{2} m}{h^{2}}$
D

$\frac{4 π^{2} k e^{2} m}{n^{2} h^{2}}$

Solution

$U = - \frac{k e^{2}}{2 R^{3}}, F = - \frac{d U}{d R} = - \frac{3 k e^{2}}{2 R^{4}}$
$But, F = \frac{m v^{2}}{R} \Rightarrow \frac{m v^{2}}{R} = \frac{3 k e^{2}}{2 R^{4}}$
$Also, m v R = \frac{n h}{2 π}$
$Solve to get: R = \frac{6 π^{2} k e^{2} m}{n^{2} h^{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App