If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength i, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be (assume kinetic energy of ejected photoelectron to be very high in comparison to work function):

Options

A. `(4)/(9)lambda`
B. `(3)/(4)lambda`
C. `(1)/(2)lambda`
D. `(2)/(3)lambda`

Answer

A

Explanation

`E=W+KE_("max")," "(hc)/(lambda)=W+(P^(2))/(2m)`
`(Wrarr0)," "(lambda_(2))/(lambda_(1))=(P_(1)^(2))/(P_(2)^(2))`
`(lambda_(2))/(lambda)=(P^(2))/((1.5P)^(2))," "(lambda_(2))/(lambda)=(4)/(9)`