If the momentum of an electron is changed by `p`, then the de - Broglie wavelength associated with it changes by `0.5 %`. The initial momentum of electron will be

Options

A. `200P`
B. `400P`
C. `P/200`
D. `100P`

Answer

a

Explanation

WE know that `lambda=h/P :. Dlambda=-h/(P^(2))dP`,
`(dlambda)/lambda=(-h/(P^(2))dP)/(h//P)=-(dP)/P=(dP)/P` (in magnitude) Given `(dlambda)/lambda=0.5/100 , dP=P`.
Let the initial momentum be `P_(0)`.
Then `P/(P_(0))=(dlambda)/lambda=0.5/100` or `P_(0)=100/0.5P=200P`