Two identical photocathodes receive light of frequency `f_(1) andf_(2)` if the velocites of the photo electrons (of mass `m`) coming out are repectively `v_(1) and v_(2)` then

Options

A. `v_(1) - v_(2) = [ ( 2h)/(m) (f_(1) - f_(2))]^(1//2)`
B. `v_(1)^(2) - v_(2)^(2) = ( 2h)/(m) (f_(1) - f_(2))`
C. `v_(1) + v_(2) = [ ( 2h)/(m) (f_(1) + f_(2))]^(1//2)`
D. `v_(1)^(2) + v_(2)^(2) = ( 2h)/(m) (f_(1) + f_(2))`

Answer

B

Explanation

Using Einstein photoelectric equation
`E = W_(0) + K_(max)`
`hf_(1) = W_(0) + (1)/(2) mv_(1)^(2)` ….(i)
`hf_(1) = W_(0) + (1)/(2) mv_(2)^(2)` …..(ii)
`rArr h(f_(1) - f_(2)) = (1)/(2) mv(v_(1)^(2) - v_(2)^(2))`
`rArr (v_(1)^(2) - v_(2)^(2)) = (2h)/(m) (f_(1) - f_(2))`