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. `lamda'` is less than `(lamda)/(2)`
B. `lamda'` is greater than `(lamda)/(2)`
C. `lamda'` is greater than `(lamda)/(2)` but less than `lamda`
D. `lamda'` is exactly equal to `(lamda)/(2)`.

Answer

C

Explanation

Energy of photoelectron,
`E=(hc)/(lamda)-W implies (hc)/(lamda)=E+W` . .. (i)
Where, W is the work function for the metal surface (constant).
`2E=(hc)/(lamda')-W implies (hc)/(lamda')=2E+W` . . (ii)
Dividing eq. (i) by (ii) we get
`(lamda')/(lamda)=(E+W)/(2E+W)=((E+W))/(2(E+(W)/(2)))`
`because (lamda')/(lamda) gt (1)/(2) or lamda' gt (lamda)/(2)" "therefore lamda gt lamda' gt (lamda)/(2)`.