Question

The work functions of two metals are 2.75 eV and 2 eV respectively. If these are irradiated by photons of energy 3 eV, the ratio of maximum momenta of the photoelectrons emitted respectively by them is

• A. 1:2
• B. 1:3
• C. 1:4
• D. 2:1
• E. 4:1

Hint:

When asked for a ratio of momenta, always calculate the kinetic energies first. The momentum ratio is simply the square root of the energy ratio.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Einstein's photoelectric equation relates the energy of incident photons to the work function of the metal and the maximum kinetic energy of the emitted electrons. Momentum can then be derived from the kinetic energy.
Step 2: Key Formula or Approach:
1. Einstein's Equation: \( K_{max} = E_{photon} - \phi \)
2. Relation between Momentum (\( p \)) and Kinetic Energy (\( K \)): \( p = \sqrt{2mK} \implies p \propto \sqrt{K} \).
Step 3: Detailed Explanation:
1. For Metal 1: \[ K_1 = 3 \text{ eV} - 2.75 \text{ eV} = 0.25 \text{ eV} \] 2. For Metal 2: \[ K_2 = 3 \text{ eV} - 2 \text{ eV} = 1 \text{ eV} \] 3. Calculate the ratio of momenta: \[ \frac{p_1}{p_2} = \sqrt{\frac{K_1}{K_2}} \] \[ \frac{p_1}{p_2} = \sqrt{\frac{0.25}{1}} = \sqrt{0.25} \] \[ \frac{p_1}{p_2} = 0.5 = \frac{1}{2} \]
Step 4: Final Answer:
The ratio of the maximum momenta is 1:2.