Answer :

In photoelectric effect an electromagnetic radiation (Can be Visible Light) is incident on a metal, if the energy of incident radiation is more than work function of the metal, then electrons are ejected out of the metal surface with some kinetic energy


Work function is the minimum Energy required to just pull out an electron from metal surface.


the setup for photoelectric effect has been shown in figure



Now the energy supplied to electron through photon (assuming light to be particle) is used up in overcoming the internal atomic forces to come to surface of metal (equal to work function of metal) and end extra energy is converted to kinetic energy of particle


So the maximum kinetic energy of an electron can be given by the photoelectric equation


Kmax = E – ϕo


Where Kmax is the maximum kinetic energy of electron.


E is the energy of incident radiation.


ϕo is the work function of metal.


We know energy of an electromagnetic radiation can be given by relation


E = h𝜈


Where h is Planck’s constant.


𝜈 is the frequency of radiation.


So, above equation becomes


Kmax = h𝜈 ϕo


Now to stop the moving electrons a potential difference is such applied which applies force in opposite direction to the motion, if the energy transferred to electron due to potential difference in equal to maximum kinetic energy of electron then the electrons completely stop moving. We know energy transferred or work done by a potential difference on a charged particle is given by relation


W = qVo


Where W is the energy transferred by a potential difference of Vo volts to a charge particle having charge q


Now for electrons to completely stop we have,


Kmax = W


Or Kmax = qVo


Since particle is electron so we have


q = e


e is charge of electron, e = 1.6 × 10-19 C


i.e. Kmax = eVo


So, the photoelectric equation becomes


eVo = h𝜈 ϕo


or we can say the work function is given as


ϕo = h𝜈 – eVo


where Vo is stopping Potential Difference


we know the relation for any electromagnetic wave we have


c = 𝜈𝜆


Where 𝜈 is the frequency and 𝜆 is wavelength of electromagnetic radiation having velocity C


So, re arranging we get


𝜈 = c/𝜆


So the photo electric equation becomes


ϕo = hc/𝜆 – eV


We know value of Planck’s constant


h = 6.6 × 10-34Js


charge of electron


e = 1.6 × 10-19 C


the speed of light


C = 3 × 108 m/s


light is incident from argon laser Light of wavelength


𝜆 = 488 nm = 488 × 10-9 m


We are given the stopping potential difference


Vo = 0.38 V


Putting thse values in equation to find work function of emitter ϕo


ϕo = hC/𝜆 – eVo


we have



We get


ϕo = 4.05 × 10-19J – 0.608 × 10-19 J = 3.46 × 10-19J


so work function of emitter metal is 3.46 × 10-19J


converting it to eV


1 eV = 1.6 × 10-19J


i.e.


1J = (1/1.6 × 10-19)eV


So we get work function of emitter metal as



We get ϕo = 2.16 eV


So the work function of emitter metal is 2.16 eV


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