In a photocell bi chromatic light of wave length 2480 A° and 6000 A° are incident on a cathode whose work function is 4.8 eV. If a uniform magnetic field of 3 × 10^-5 T exists parallel to the plate, find the radius of the circular path described by the photoelectron.

Q: In a photocell bi chromatic light of wave length 2480 A° and 6000 A° are incident on a cathode whose work function is 4.8 eV. If a uniform magnetic field of 3 × 10-5 T exists parallel to the plate, find the radius of the circular path described by the photoelectron. (mass of electron is 9 ×10-31 kg)

Sol: $\large E_1 = \frac{12400}{\lambda_1} = \frac{12400}{2480}$

E1 = 5 eV

$\large E_2 = \frac{12400}{\lambda_2} = \frac{12400}{6000}$

E2 = 2.06 eV

As E2 < W0 and E1 > W0 ,

Emission is possible only with  λ1

Maximum K.E of emitted photo electrons ,

K = E1 – W0 = 0.2 eV

Photo electrons experience magnetic force and move along a circular path of radius.

$\large r = \frac{m v}{q B} = \frac{\sqrt{2 m K}}{q B}$

r = 5 cm