Light of frequency `8.41xx10^(14)Hz` is incident on a metal surface. Electrons with their maximum speed of `7.5xx10^(5)ms^(-1)` are ejected from the surface. Calculate the threshold frequency for photoemission of electrons. Also find the work function of the metal in electron volt `(eV)`. Given Plank's constant `h=6.625xx10^(-34)Js` and mass of the electron `9.1xx10^(-31)kg`.

Explanation

`v = 8.41 times 10^(14)Hz`
`v_(max) = 7.5 times 10^(5)ms^(-1)`
`h = 6.625 times 10^(-34)Js^(-1)`
`m = 9.1 times 10^(-31)kg`
`hv = O/_(0) K_(max)`
`hv = hv_(0) + (1)/(2) m v_(max)^(2)`
`hv - hv_(0) = (1)/(2) m v_(max)^(2)`
`(v-v_(0)) = (1)/(2h) mv_(max)^(2) = (1)/(2 times 6.625 times 10^(-34)) times 9.1 times 10^(31) times (7.5 times 10^(5))^(2)`
`(v-v_(0)) = 3.8632 times 10^(14)`
`v_(0) = 3.8632 times 10^(14) - 8.41 times 10^(14) = 4.5468 times 10^(14) Hz`
`phi_(0) = hv_(0) = 6.625 times 10^(-34) times 4.5468 times 10^(14) = 3.01226 times 10^(-19)`
`phi_(0) = (3.0122 times 10^(-19))/(1.6 times 10^(-19)) = 1.8826eV`