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Which of the following equations does re...

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)

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
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)))`
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Knowledge Check

  • When a certain metal was irradiated with light of frequency 40xx10^(16) s^(-1) , the photoelectrons emitted had four times kinetic energy as the kinetic energy of photoelectrons emitted when the same metal was irradiated with light of frequency 2.0 xx 10^(16) s^(-1) . the trhreshold frequency ( v_(0) ) of the metal in s^(-1) is

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  • In a photoelectric effect experiment, the kinetic energy of an emitted electron is 1.986 xx 10^(-19) J , when a radiation of frequency 1.0 xx 10^15 s^(-1) hits the metal. What is the threshold frequency of the metal (in s^(-1) )?(Planck's constant = 6.62 xx 10^(-34) Js)

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