Question

When a metal of work function $4\text{ eV}$ is exposed to radiation, the maximum kinetic energy of the emitted electrons is $4\text{ eV}$. The stopping potential required is:

• A. $1.4\text{ V}$
• B. $2.8\text{ V}$
• C. $0.2\text{ V}$
• D. $0.4\text{ V}$

Hint:

When kinetic energy is given in electron-volts ($\text{eV}$), finding the stopping potential is immediate—simply strip away the "e" character from the unit tag! A maximum kinetic energy of $0.4\text{ eV}$ always requires a stopping potential of exactly $0.4\text{ Volts}$.

Answer 1

The Correct Option is D

Concept: The stopping potential ($V_0$) is defined as the retarding electrical potential difference required to completely halt the most energetic photoelectrons from reaching the receiving electrode plate. It relates directly to the maximum kinetic energy ($K_{\text{max}}$) of the emitted charge carriers through the fundamental charge equation: \[ K_{\text{max}} = e \cdot V_0 \]

Step 1: Extract variables and apply matching charge definitions.
We are given that the maximum kinetic energy is: \[ K_{\text{max}} = 0.4\text{ eV} \] Substituting this energy value directly into our definition: \[ 0.4\text{ eV} = e \cdot V_0 \] Dividing out the fundamental electron charge factor ($e$) from both sides: \[ V_0 = 0.4\text{ V} \]