Potential energy between a proton and an electron is given by U = K e 2 3 R 3 , then radius of Bohr's orbit can be given by

Question

Aicharya · Accepted Answer

Since electrostatic force is a conservative force, therefore, $F = - \frac{d U}{d x}$

$\Rightarrow F = - \frac{d U}{d R} = \frac{K e^{2}}{R^{4}}$

This force provides the necessary centripetal force, $F_{C} = \frac{m v^{2}}{R}$

$\Rightarrow \frac{K e^{2}}{R^{4}} = \frac{m v^{2}}{R} \Rightarrow v^{2} = \frac{K e^{2}}{m R^{3}}$

Using Bohr quantization of angular momentum theory,

$\Rightarrow m v r = \frac{n h}{2 π} \Rightarrow r = \frac{4 π^{2} K e^{2} m}{n^{2} h^{2}}$

Thus, Bohr's orbit is, $r = \frac{4 π^{2} K e^{2} m}{n^{2} h^{2}}$

Potential energy between a proton and an electron is given by U = K e 2 3 R 3 , then radius of Bohr's…