First slide

Photoelectric effect and study of photoelectric effect

Question

Radiation, with wavelength 6561 $A^{0}$ falls on a metal surface to produce photoelectrons . The electrons are made to enter a uniform magnetic field of $3 \times 10^{- 4} T$ . If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal close to:

Moderate

A

$1.8 e V$
B

$0.8 e V$
C

$1.1 e V$
D

$1.6 e V$

Solution

$\begin{array}{l} I n c i d e n t E n e r g y, E_{i} = \frac{12400}{λ (i n \overset{0}{A})} = \frac{12400}{6561} = 1.89 e V \\ R a d i u s o f C i r c l e, r = \frac{m v}{B e} = \frac{\sqrt{2 m K}}{B e} \\ \Rightarrow K = \frac{r^{2} B^{2} e^{2}}{2 m} = \frac{{(10 \times 10^{- 3})}^{2} \times {(3 \times 10^{- 4})}^{2} \times {(1.6 \times 10^{- 19})}^{2}}{2 \times 9.1 \times 10^{- 31}} J \times \frac{1 e V}{1.6 \times 10^{- 19} J} = 0.79 e V \\ ∴ W o r k f u n c t i o n = E_{i} - K = 1.1 e V \end{array}$

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