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

If E is the energy of incident photon and W the work function, then `E_W_0="available energy"`
`E-W_0=(1)/(2)mv^(2)`
or `v=sqrt((2(E-W_0))/(m))`
`(v_1)/(v_2)=sqrt((1-0.5)/(2.5-0.5))=sqrt((0.5)/(2))=(1)/(2)`