Question

The threshold wavelengths for photoelectric emission from two metals A and B are 400 nm and 800 nm respectively. The ratio of their work functions \(\phi_A\) to \(\phi_B\) is

• A. \( \dfrac{1}{2} \)
• B. \( 4 \)
• C. \( \dfrac{1}{4} \)
• D. \( 2 \)

Hint:

Work function is inversely proportional to threshold wavelength.

Answer 1

The Correct Option is D

Step 1: Relation between work function and threshold wavelength.
Work function is given by \[ \phi = \frac{hc}{\lambda_0}. \]
Step 2: Writing ratio of work functions.
\[ \frac{\phi_A}{\phi_B} = \frac{\lambda_B}{\lambda_A}. \]
Step 3: Substituting given values.
\[ \frac{\phi_A}{\phi_B} = \frac{800}{400} = 2. \]
Step 4: Conclusion.
The ratio of work functions is \(2\).