If photo-electric effect,when frequency of incident radiation is doubled ,maximum speed of electron emitted also becomes double .work function of metal will be……

Options

A. `(hv)/(4)`
B. `(hv)/(3)`
C. `(hv)/(2)`
D. `(2hv)/(3)`

Answer

D

Explanation

Initially `(1)/(2)mv^(2)=hv-phi` ……(1)
Now ,if frequency and speed both become double,
`(1)/(2)m(2v)^(2)=h(2v)-phi`
`4((1)/(2)mv^(2))=2hv-phi`
`4(hv-phi)=hv-phi` [From result (1)]
`therefore 4hv-4phi=2hv-phi`
`therefore 2hv=3phi`
`therefore phi=(2hv)/(3)`