Question

In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10 $cm$ and are connected through an ammeter without any cell.

A magnetic field $B$ exist 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.

• A. $B=2.85\times {10}^{-5}T$
• B. $B=3.25\times {10}^{-5}T$
• C. $B=4.23\times {10}^{-5}T$
• D. $B=7.88\times {10}^{-5}T$

Answer 1

The correct option is A

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

Given ,separation between the collector and emitter, d=10 $cm$

Work function , $\varphi =2.39$ $eV$

Wavelength range, ${\lambda }_1=400nm$ to ${\lambda }_2=600nm$

Magnetic field $B$ will be minimum if energy is maximum. For maximum energy, wavelength $\lambda$ should be minimum. Einstein’s photoelectric equation:

$E=hc/\lambda -\varphi =3.105-2.39=0.715eV$

The beam of ejected electrons will be bent by the magnetic field. If the electron do not reach the other plates, there will be no current.

When a charged is sent perpendicular to a magnetic field, it move along a circle of radius,

$r=mv/qB$

Radius of the circle should be equal to $r=d=10cm$, so that no current flows in the circuit.

$r=\frac{\sqrt{2mE}}{qB}$

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