When a metal surface is illuminated by light wavelengths `400 nm` and `250 nm` , the maximum velocities of the photoelectrons ejected are `upsilon` and `2 v` respectively . The work function of the metal is
`( h = "Planck's constant" , c = "velocity of light in air" )`

Options

A. `2 hc xx10^6 J`
B. `1.5hc xx10^6 J`
C. `hc xx10^6 J`
D. `0.5hc xx10^6 J`

Answer

A

Explanation

`K_("max") =(hc)/lamda -phi_0`
`implies1/2mv^2 =(hc)/(400 xx10^(-9))-phi_0 " "...(i)`
and `implies1/2m(2v)^2 =(hc)/(250 xx10^(-9))-phi_0 " "...(ii)`
From (i) and (ii)
`(4hc)/(400 xx10^(-9))-4phi_0 =(hc)/(250xx10^(-9))-phi_0`
`implies phi_0 = 2 hc xx10^6 J`