An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' - '. The rate of change of deBroglie wave length associated with the electron varies inversely as n…

Question

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

Accepted Answer

Correct answer: 2. (2) Let the momentum of e^-at any time t is p and its de-broglie wavelength is . Then, p= h dp dt= -h ^2 dλ dt ma=F=- h dλ dt [ m= mass ofe ] Where, -ve sign represents decrease in with time ma= -h ( h/p )^2 dλ dt a=- p^2 mh dλ dt a=- mv^2 h dλ dt dλ dt=- ah mv^2 … … … … (i ) here, a= qEm= em 2 _0 a= σe2 m _0 and v=u+ at Substituting values of a ∖ \& v in equation (i) dλ dt=- 2 h _0 t^2 ⇒ dλ dt ∝ 1t^2 ⇒n=2

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

Solution

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