An electron is continuonsly accelerated in vacume tube by appliying potential difference if its de Brogle wavelength is decresed by `1%` the change in the kinetic energy of the electron is nearly

Options

A. Decreased by `1%`
B. Increased by `2%`
C. Increased by `1%`
D. Decreased by `2%`

Answer

B

Explanation

`(hc)/(lambda)=E_(1)-E_(2)=KE_(2)-KE_(1)`
`:. Lambda=h/(mV) (mV)^(2)=(h/lambda)^(2), 1/2 mV^(2)=1/(2m)h^(2)/lambda^(2)`
`:. (hc)/lambda=h^(2)/(2m lambda_(2)^(2))-h^(2)/(2mlambda_(1)^(2)) :. Lambda=(2mc)/(h){(lambda_(1)^(2)lambda_(2)^(2))/(lambda_(1)^(2)-lambda_(2)^(2))}`