Question

In an experiment on photo electric effect, the emitter and the collector plates are placed at a separation of 10 cm and are connected through an ammeter without any cell (figure 42-E3). A magnetic field B exists parallel to the plates. The work function of the emitter is 2.39 eV and the light incident on it has wavelengths between 400 nm and 600 nm. Find the minimum value of B for which the current registered by the ammeter is zero. Neglect any effect of space charge.

Answer 1

Here ${\varphi }_0=2.39eV$

${\lambda }_1=400nm,$

${\lambda }_2=600mn,$

for b to be minimum, energy should be maximum

$\therefore \lambda$ should be minimum

$E=\frac{hc}{\lambda }-{\varphi }_0$

$=\frac{1242}{400}-2.39$

$=3.105-2.39=0.715eV.$

The presence of magnetic field will bend the beam. There will be no current if the electron does not reach the other plates

$r=\frac{mv}{qB}$

$\Rightarrow r=\sqrt{\frac{2mF}{qB}}$

$\Rightarrow 0.1=\sqrt{\frac{2\times 9.1\times {10}^{-31}\times 1.6\times {10}^{-19}\times 0.715}{1.6\times {10}^{-19}\times B}}$

$B=\sqrt{\frac{2\times 9.1\times 1.6\times 0.715\times {10}^{-50}}{1.6\times {10}^{-20}}}$

$=\sqrt{\frac{2\times 9.1\times 1.6\times 0.715}{1.6}}\times {10}^{-5}$

$=2.85\times {10}^{-5}$