Question

A light beam of frequency v incident on a metal
of work function 0, which is kept in region of
uniform magnetic field B. What will be greatest
radius of circle traced by photo electrons :-
(options are above in the attachment)​

Answer 1

Greatest radius of circle will be  (3) √ [2 m (hν - Φ ) ]  / eB

Explanation:

the energy of the light beam with frequency ν is = hν

now we know that

energy of light beam = work function (Φ) + K E  (kinetic energy of photoelectron  )

(hν - Φ ) =   K E of photoelectron   .......................................... equation 1

K E = 1/2 m V²

V = $\sqrt{2 K E / m}$

V= √ [2 (hν - Φ ) / m ]   .......................................... equation 2

Ф   ν   Φ

when kept in uniform magnatic field B, for tracing circular motion

Magnetic force = centrifugal force

e B V = mV² / r            ....................................... equation 3        

where V is the velocity , r is the radius , e is the charge of electron , m is mass of electron

simplifying equation  2 we get  

r =  m V / B e

using equation 2 in equation 3 we get

r = √ [2 m (hν - Φ ) ]  / eB

option 3