Lights of two different frequencies whose photons have energies 1 and 2.5 eV, respectively, successively illuminate a metal whose work function is 0.5 eV. The ratio of the maximum speeds of the emitted electrons

Options

A. `1 : 4`
B. `1 : 2`
C. `1 : 1`
D. `1 : 5`

Answer

B

Explanation

We have `(1)/(2) mv_(max)^(2) = E - phi`
Here case (i) `(1)/(2) mv_(1 max)^(2) = (1 - 0.5) eV`
`(1)/(2) mv_(2 max)^(2) = (2.5 - 0.5) eV`
Hence , `(v_(1 max)^(2))/(v_(2 max)^(2)) = (1)/(4)`
`(v_(1 max))/(v_(2 max)) = (1)/(2)`