Radiation of wavelength `lambda` in indent on a photocell . The fastest emitted electron has speed `v` if the wavelength is changed to `(3 lambda)/(4)` , then speed of the fastest emitted electron will be

Options

A. `gtv((4)/(3))^(1//2)`
B. `ltv((4)/(3))^(1//2)`
C. `=v((4)/(3))^(1//2)`
D. `=v((3)/(4))^(1//2)`

Answer

A

Explanation

`E=E_(0)+(1)/(2)mv^(2)`
`(hc)/(lamda)=E_(0)+(1)/(2)mv^(2)` . . . . .(i)
`(hc)/((3lamda//4))=E_(0)+(1)/(2)mv^('2)`
`(4)/(3)(hc)/(lamda)=E_(0)+(1)/(2)mv^('2)` . . . .(ii)
Equation (i)`xx(4)/(3)`- equation (ii),
`[(4)/(3)(hc)/(lamda)-(4)/(3)(hc)/(lamda)]=(4)/(3)[E_(0)+(1)/(2)mv^(2)mv^(2)]-[E_(0)+(1)/(2)mv^('2)]`
`(1)/(2)mv^('2)=(w)/(3)+(4)/(3)xx(1)/(2)mv^(2)`
`(1)/(2)mv^('2) gt (4)/(3)xx(1)/(2)mv^(2)`
`v'gtsqrt((4)/(3))` v