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:
Show 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 $0.4\text{ Volts}$.
Understanding the 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:
\[
V_0 = 0.4\text{ V}
\]