First slide

Photoelectric effect and study of photoelectric effect

Question

In a photocell, bi-chromatic rays of light of wavelength 2475 $Å$ and 6000 $Å$ are incident on cathode whose work function is 4.8 eV. If a uniform magnetic field of 3 x 10^-5
tesla exists parallel to the plate, the radius of the path describe by the photoelectron will be (mass of electron =9 x 10^-31 kg)

Moderate

A

1 cm
B

5 cm
C

10 cm
D

25 cm

Solution

Energy of photons corresponding to light of wave length $λ_{1} = 2475 Å is E_{1} = \frac{12375}{2475} = 5 eV$
and that corresponding to $λ_{2} = 6000 Å$ is
$\begin{array}{l} E_{2} = \frac{12375}{6000} = 2.06 eV \\ As E_{2} < W_{0} and E_{1} > W_{0} \end{array}$
photoelectric emission is possible with $λ_{1}$ only. Maximum kinetic energy of emitted photoelectrons, $K = E - W_{0} = 5 - 4.8 = 0.2 e V$
Photo electrons experience magnetic force and move along a circular path of radius,
$\begin{matrix} r = \frac{m v}{q B} = \frac{\sqrt{2 m K}}{q B} = \frac{\sqrt{2 \times 9 \times 10^{- 31} \times 0.2 \times 1.6 \times 10^{- 19}}}{1.6 \times 10^{- 19} \times 3 \times 10^{- 5}} = 0.05 m = 5 cm . \end{matrix}$

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