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

Answer

A

Explanation

For one photocathode
`hf_(1) - W = (1)/(2) m nu _(1)^(2)` ….(i)
`for another photo cathode
`(hf_(2) - W = (1)/(2) m nu _(2)^(2)` ….(ii)
sobtracting (ii) from (i) we get
`(hf_(1) - W) -(hf_(2) - W) = (1)/(2) m nu _(1)^(2) - (1)/(2)m nu _(2)^(2) `
`h(f_(1) - (f_(2) = (m)/(2)(nu _(1)^(2) - nu _(2)^(2))`
` :. (nu _(1)^(2) - nu _(2)^(2)) = (2b)/(m) (f_(1) - (f_(2))`