Q. 113.9( 17 Votes )

# Light of waveleng

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

K_{max} = E – ϕ_{o}

Where K_{max} is the maximum kinetic energy of electron.

E is the energy of incident radiation.

ϕ_{o} 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

K_{max} = h𝜈 – ϕ_{o}

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 = qV_{o}

Where W is the energy transferred by a potential difference of V_{o} volts to a charge particle having charge q

Now for electrons to completely stop we have,

K_{max} = W

Or K_{max} = qV_{o}

Since particle is electron so we have

q = e

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

i.e. K_{max} = eV_{o}

So, the photoelectric equation becomes

eV_{o} = h𝜈 – ϕ_{o}

or we can say the work function is given as

ϕ_{o} = h𝜈 – eV_{o}

where V_{o} 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

ϕ_{o} = hc/𝜆 – eV

We know value of Planck’s constant

h = 6.6 × 10^{-34}Js

charge of electron

e = 1.6 × 10^{-19} C

the speed of light

C = 3 × 10^{8} 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

V_{o} = 0.38 V

Putting thse values in equation to find work function of emitter ϕ_{o}

ϕ_{o} = hC/𝜆 – eV_{o}

we have

We get

ϕ_{o} = 4.05 × 10^{-19}J – 0.608 × 10^{-19} J = 3.46 × 10^{-19}J

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

converting it to eV

1 eV = 1.6 × 10^{-19}J

i.e.

1J = (1/1.6 × 10^{-19})eV

So we get work function of emitter metal as

We get ϕ_{o} = 2.16 eV

So the work function of emitter metal is 2.16 eV

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