Which of the following equations does represent the velcity (v) of the ejected electrons when a metal is made to strike with light of frequency v and threshold frequency of the metal is `v_(0)` ?
( `m_(e)` = mass of electron and h is Plank's constant)

Options

A. `v = sqrt((h(v-v_(0)))/(m_(e)))`
B. `v = sqrt((2h(v-v_(0)))/(m_(e)))`
C. `v = sqrt((h(v-v_(0)))/(2m_(e)))`
D. `v = sqrt(h (v - v_(0))m_(e))`

Answer

B

Explanation

Following the law of conservation of energy principle, the KE of the ejected electron is given by the equation ,
`hv = hv_(0) +(1)/(2) m_(e) v^(2) or h(v-v_(0))=(1)/(2)m_(e) v^(2) " ". . . (i)`
where, hv = energy of striking photon
`hv_(0)` = minimum energy required to eject the electron
`m_(e)` = mass of electron
v = velocity of the ejected electron
Thus , from E. (i) , the velocity of the ejected electron is given by the following equation ,
` v = sqrt((2h(v - v_(0)))/(m_(e)))`