An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' - '. The rate of change of de-Broglie wave length associated with the electron varies inversely as n ^ th power of time. The numerical value of n is ________.

Step-by-step solution

Let the momentum of e ⁻ at any time t is p and its de-broglie wavelength is . Then, p = h aligned & dp dt = - h ^2 ~d dt & ma = F =- h ~d dt [ ~m = mass of e ] aligned Where, -ve sign represents decrease in with time ma = - h ( ~h / p )^2 ~d dt aligned & a =- p ^2 mh ~d dt & a =- mv ^2 ~h ~d dt & ~d dt =- ah mv ^2 ...(1) aligned here, a = qE m = e m 2 ₀ a = e 2 ~m ₀ and v = u + at v = at Substituting values of a & v in equation (1) aligned & d dt =- 2 ~h ₀ et ^2 & ~d dt 1 t ^2 & n =2 aligned