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

de Broglie wavelength , `lamda = (h)/(sqrt(2mE))`
`E=(h^2)/(2mlamda^2)`
or `E = h^2/(2mlamda^(2)) " or "E prop 1/lamda^2`
`:. (E.)/E = lamda^2/(lamda.2)=(1/(0.5))^(2) = 4 " or " E. = 4E`
The energy should be added to decrease the wavelength
`= E. - E = 4E - E = 3E`