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. `v(3//4)^(1//2)`
B. `v(4//3)^(1//2)`
C. less than `v(4//3)^(1//2)`
D. greater than `v(4//3)^(1//2)`

Answer

D

Explanation

`(hc)/(lambda) =phi +(1)/(2)mv^(2)`
`(hc)/(3lambda//4) =phi +(1)/(2)mv_(1)^(2)`
`(v_(1)^(2))/(v^(2)) =((4hc)/(3lambda)- phi)/((hc)/(lambda)- phi) =((hc)/(lambda)+(1)/(3)(hc)/(lambda) -phi)/((hc)/(lambda) -phi)`
`=(((hc)/(lambda)- phi)/((hc)/lambda-phi)) + (((1)/(3)(hc)/(lambda))/((hc)/(lambda)-phi))`
`=1+ (gt(1)/(3)) = gt(4)/(3)`
`v_(1) gt v sqrt((4)/(3))`