The energy that should be added to an electron to reduce its de - Broglie wavelength from one `nm to 0.5 nm` is

Options

A. Four times the initial energy
B. Equal to the initial energy
C. Twice the initial energy
D. Thrice the initial energy

Answer

D

Explanation

`l = (ħ)/(sqrt( 2m E)) , (lambda')/(lambda) sqrt(E/(E')) = ((0.5)/(1))^(2)`
`rArr E' = ( E )/(0.25) = 4 E`
The energy should be added to decrease wavelength .
`= E' - E = 3 E`