Light of wavelength `lamda` strikes a photoelectric surface and electrons are ejected with kinetic energy K. If K is to be increased to exactly twice its original value, the wavelength must be changed to `lamda'` such that

Options

A. `lambda' lt lambda//2`
B. `lambda gt lambda//2`
C. `lambda gt lambda' gt lambda//2`
D. `lambda' = lambda//2`

Answer

C

Explanation

`(hc)/(lambda') = 2 epsilon + phi`
`(hc)/(lambda) = epsilon + phi`
dividing length, `(lambda')/(lambda) = (epsilon +phi)/(2 epsilon + phi)` or `(lambda')/(lambda) lt 1`, so `lambda' lt lambda`
Also, `(lambda')/(lambda) = (1)/(2) [(epsilon+phi)/(epsilon+(phi)/(2))]`
`(lambda')/(lambda) gt (1)/(2)` or `lambda lt lambda' lt (lambda)/(2)`