The photo cathode and collector plate are kept 10 cm apart and connected through a galvanometer without a battery. A magnetic field B exists parallel to the plates. The work function of the emitter is 2.39 $e V$ and the light incident on it has wavelength 400 to 600 $n m$ . Find the minimum value of $B$ so that galvanometer shows null deflection.

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Solution

$(K E)_{m a x} = h f - ϕ$ or
$(K E)_{m a x} = 3.1 - 2.39 = 0.71$ $e V$
$r = \frac{m v}{q B}$
$B = \sqrt{\frac{2 (K E) m}{q r}}$
$B = \sqrt{\frac{2 (0.71 t i m e s 1.6 \times 10^{- 19}) \times 9 \times 10^{- 31}}{1.6 \times 10^{- 19} \times 1}}$
$= 2.85 \times 10^{- 5} T$

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