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The light of wavelength 4,125 Å is inci...

The light of wavelength `4,125 Å` is incident on a metal surface of work function `phi` The emitted photoelectrons describe a circle of radius 200 cm under the effect of a magnetic field of flux density `1/sqrt7xx10^(-5)` tesla. If charge to mass ratio for electron is `1.7xx10^(11)` , find the value of `phi`.
`{:(0,1,2,3,4,5,6,7,8,9):}`

Text Solution

Verified by Experts

The correct Answer is:
[1]
If K is the kinetic energy of electron, then radius of circular path described by electron in a magnetic field of flux density B is
`r=(sqrt(2mK))/(qB)`
`implies K=(q^2B^2r^2)/(2m)=(q/m)(qB^2r^2)/2`
Given, `q/m=1.7xx10^(11) , q = 1.6 xx10^(-19) C,`
`B = 1 /sqrt(17)xx10^(-5) T`
r = 200 cm = 2 m
`:.K=1/2xx1.7xx10^(11)xx1.6xx10^(-19)xx(1/sqrt17xx10^(-5))^2xx2^2`
`=32xx10^(-20)J = 2 eV`
Also, energy of incident photons , `E =(hc)/lamda=3eV`
Using , `E = W + K`
`W = E - K = 3 - 2 = 1 eV`
`phi = 1`
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