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

Step-by-step solution

Since electrostatic force is a conservative force, therefore, F = - d U d x ⇒ F = - d U d R = K e 2 R 4 This force provides the necessary centripetal force, F C = m v 2 R ⇒ K e 2 R 4 = m v 2 R ⇒ v 2 = K e 2 m R 3 Using Bohr quantization of angular momentum theory, ⇒ m v r = n h 2 π ⇒ r = 4 π 2 K e 2 m n 2 h 2 Thus, Bohr's orbit is, r = 4 π 2 K e 2 m n 2 h 2