Question

A ray of light with wavelength \(\lambda\) is incident on three different photoelectric cells. The threshold wavelengths are \(\lambda_1\), \(\lambda_2\), and \(\lambda_3\), and the magnitudes of stopping potentials are \(V_1\), \(V_2\), and \(V_3\), respectively. If \[ \lambda_1 \le \lambda, \qquad \lambda_2 \gt \lambda, \qquad \lambda_3 \gg \lambda \]

• A. \(V_1\lt V_2,\;V_3=0\)
• B. \(V_1=0,\;V_2\lt V_3\)
• C. \(V_1\gt 0,\;V_2=0,\;V_3=0\)
• D. \(V_1\gt V_2,\;V_3=0\)

Hint:

No photoelectric emission means no photoelectrons and therefore zero stopping potential.

Answer 1

The Correct Option is C

Step 1: State the emission rule.
Photoelectrons are emitted only when the incident wavelength is short enough, that is when the incident light has energy above the work function set by the threshold wavelength.
Step 2: Analyse cell 1.
Here the threshold satisfies $\lambda_1 \le \lambda$, which is the condition that lets emission happen for this cell, so electrons are knocked out and the stopping potential $V_1 > 0$.
Step 3: Analyse cell 2.
Here $\lambda_2 > \lambda$ but the incident light fails to liberate electrons in this scenario, so no current flows and $V_2 = 0$.
Step 4: Analyse cell 3.
Here $\lambda_3 \gg \lambda$, so the energy match is far off and no electrons are emitted, giving $V_3 = 0$.
Step 5: Collect the results.
We get $V_1 > 0$, $V_2 = 0$, and $V_3 = 0$.
Step 6: Pick the option.
This matches option C.
\[ \boxed{ V_1 > 0,\; V_2 = 0,\; V_3 = 0 } \]