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

Concept: Photoelectric emission occurs only when \[ \lambda \le \lambda_0 \] where \(\lambda_0\) is the threshold wavelength.

Step 1: Analyze cell 1.
\[ \lambda_1 \le \lambda \] Hence photoelectric emission occurs. Therefore, \[ V_1\gt 0 \]

Step 2: Analyze cell 2.
No photoelectric emission occurs. Thus, \[ V_2=0 \]

Step 3: Analyze cell 3.
Since \[ \lambda_3\gg\lambda \] the incident wavelength is insufficient to cause emission. Hence, \[ V_3=0 \]

Step 4: Choose the correct option.
\[ V_1\gt 0, \qquad V_2=0, \qquad V_3=0 \] \[ \boxed{\text{Option (C)}} \]