Question

If a radiation of energy \( 4.25 \, \text{eV} \) falls on a metal surface, then the maximum kinetic energy of ejected electrons will be (work function of metal is \( 2.25 \, \text{eV} \)).

• A. \( 4.5 \times 10^{-16} \, \text{J} \)
• B. \( 6.5 \times 10^{-19} \, \text{J} \)
• C. \( 3.2 \times 10^{-19} \, \text{J} \)
• D. \( 1.6 \times 10^{-19} \, \text{J} \)

Hint:

Key points to remember:

• Photoelectric equation: \( K_{\text{max}} = h\nu
  - \phi \)
• 1 eV = \( 1.6 \times 10^{-19} \) J conversion is crucial
• Work function is the minimum energy needed to eject electrons
• Maximum KE depends on photon energy minus work function

Answer 1

The Correct Option is C

Step 1: Apply Einstein's photoelectric equation
The maximum kinetic energy \( K_{\text{max}} \) is given by: \[ K_{\text{max}} = h\nu - \phi = E - \phi \] where: - \( E = 4.25 \, \text{eV} \) (photon energy) - \( \phi = 2.25 \, \text{eV} \) (work function)
Step 2: Calculate kinetic energy in eV
\[ K_{\text{max}} = 4.25 \, \text{eV} - 2.25 \, \text{eV} = 2.00 \, \text{eV} \]
Step 3: Convert eV to Joules
Using \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \): \[ K_{\text{max}} = 2.00 \times 1.6 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-19} \, \text{J} \]
Step 4: Verify calculation
\[ 2.00 \, \text{eV} \times \frac{1.6 \times 10^{-19} \, \text{J}}{1 \, \text{eV}} = 3.2 \times 10^{-19} \, \text{J} \]
Step 5: Match with options
The calculated value matches option (c).