Question

Write down Einstein's photoelectric equation. Photons of energies 1 eV and 2.5 eV respectively are incident on a metal plate of work function 0.5 eV. If maximum kinetic energies of emitted photoelectrons are \( k_1 \) and \( k_2 \) respectively and their velocities are \( v_1 \) and \( v_2 \), then find the magnitudes of (i) \( k_1/k_2 \) and (ii) \( v_1/v_2 \).

Hint:

Kinetic energy is proportional to the square of velocity in photoelectric effect.

Answer 1

Einstein's Photoelectric Equation: \[ K_{\max} = h\nu - \phi \] 

Step 1: Using given data: \[ k_1 = 1 - 0.5 = 0.5 \, \text{eV} \] \[ k_2 = 2.5 - 0.5 = 2.0 \, \text{eV} \] \[ \frac{k_1}{k_2} = \frac{0.5}{2.0} = \frac{1}{4} \] \[ \boxed{\frac{k_1}{k_2} = \frac{1}{4}} \] 

Step 2: Since kinetic energy is proportional to the square of velocity: \[ \frac{v_1}{v_2} = \sqrt{\frac{k_1}{k_2}} \] \[ = \sqrt{\frac{1}{4}} = \frac{1}{2} \] \[ \boxed{\frac{v_1}{v_2} = \frac{1}{2}} \]