Question

If the energy of incident radiation is increased by $25\%$, the kinetic energy of the photoelectrons emitted increases from 0.6 eV to 0.9 eV. The work function of the metal is:

• A. 0.6 eV
• B. 1.2 eV
• C. 1.5 eV
• D. 1 eV

Answer 1

The Correct Option is A

Given:

• Initial kinetic energy of photoelectrons (K₁) = 0.6 eV

• After 25% increase in incident energy, new kinetic energy (K₂) = 0.9 eV

Solution:

1. Let work function be φ and initial incident energy be E.

From Einstein's photoelectric equation: \[ E = φ + K₁ \] \[ E = φ + 0.6\ \text{eV} \]

2. After 25% increase in incident energy: \[ 1.25E = φ + K₂ \] \[ 1.25E = φ + 0.9\ \text{eV} \]

3. Substitute E from first equation: \[ 1.25(φ + 0.6) = φ + 0.9 \] \[ 1.25φ + 0.75 = φ + 0.9 \]

4. Solve for φ: \[ 1.25φ - φ = 0.9 - 0.75 \] \[ 0.25φ = 0.15 \] \[ φ = \frac{0.15}{0.25} = 0.6\ \text{eV} \]