Question

In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a
perfectly absorbing cathode of work function 6.25 eV. The frequency of light is just above the threshold
frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the
photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode
and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode
experiences a force F = n x 10⁻⁴ N due to the impact of the electrons. The value of n is __________.
Mass of the electron mₑ = 9 x 10⁻³¹ kg and 1.0 eV = 1.6 x 10⁻¹⁹ J.

Answer 1

Given:

Power of monochromatic light = 200 W

Potential difference = 500 V

Work function = 6.25 eV

To find:

The force exerted due to the impact of electrons

Calculation:

As kinetic energy is zero, hv=∅

Power is given by the relation

   $Power=nhv$

   $200=n[6.25\times1.6\times 10^{-19}]$

   $n=\frac{200}{6.25\times1.6\times 10^{-19}}$      ……(1)

The photon is just above threshold and the maximum kinetic will be zero.The photons are just accelerated by a potential difference of 500 V

    $K.E_{f}=q\Delta V$

    $\frac{P^{2}}{2m}=q\Delta V$

    $P^{2}=2m\times q\Delta V$

    $P=\sqrt{2mq\Delta V}$

    $P=\sqrt{2\times9\times10^{-31}\times1.6\times10^{-19}\times 500}$     ……(2)

The number of electrons will be equal to number of photons as the efficiency is 100%

Force exerted is given by the relation

   $F=nmv$

   $F=n\times P$

By substituting the values from equations (1) & (2)

   $F= \frac{200}{6.25\times1.6\times 10^{-19}} \times \sqrt{2\times9\times10^{-31}\times1.6\times10^{-19}\times 500}$

   $F=\frac{200}{6.25\times1.6\times10^{-19}} \times\sqrt{1600\times9\times10^{-50}}$

   $F=\frac{200}{6.25\times1.6\times10^{-19}} \times120\times10^{-25}$

   $F=2400\times10^{19}\times10^{-25}$

   $F=24\times10^{-4}\ N$

Final answer:

The force exerted due to the impact of electrons is 24×10⁻⁴ N.Therefore the value of n will be 24