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

Answer

C

Explanation

`E =W + K_(max)`
`1 =0.5 +(K_(max))_(1)` `implies (K_(max))_(1) =0.5 eV`
`2.5 =0.5 +(K_(max))_(2)` `implies (K_(max))_(2) =2 eV`
`((K_(max))_(2))/((K_(max))_(1)) =((1)/(2)mv_(2)^(2))/((1)/(2)mv_(1)^(2)) =((v_(2))/(v_(1)))^(2) =(2)/(0.5) =4`
`(v_(1))/(v_(2)) =(1)/(2)`