Question

Calculate stopping potential for light of wavelength 300 nm incident on a photocathode having work function W = 3.0 eV. (h = 6.63 × 10^-34 J s, c = 3 × 10⁸ m/s, 1 eV = 1.6 × 10^-19 J)
1. 1.6 V
2. 1 V
3. 2 V
4. 1.14 V

Answer 1

Correct Answer - Option 4 : 1.14 V

Concept: Stopping potential is defined as the potential necessary to stop any electron form reaching the other side. It is a measure of the maximum kinetic energy of the electrons emitted as a result of the photoelectric effect.

work function (ϕ_o) is the minimum energy required to remove on electron form the surface of the material.

stopping potential \(\left( {{V_o}} \right) = \frac{{{{\left( {K.E} \right)}_{max}}}}{e}\)

\({\left( {K.E} \right)_{max}} = hv - {\phi _o} = \frac{{{h_c}}}{\lambda } - {\phi _o}\)

\(\Rightarrow e{V_o} = \frac{{hc}}{\lambda } - {\phi _o}\)

Calculation:

Substituting values, we get

\(e{V_0} = \left( {\frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{3 \times {{10}^{ - 7}} \times 1.6 \times {{10}^{ - 19}}}} - 3.0\;eV} \right)\) = 4.14 eV – 3 eV = 1.14 eV

So Stopping potential = 1.14 V