Question

When a metal surface is illuminated by light of wavelengths 400nm and 250nm, the maximum velocities of the photoelectrons ejected are v and 2v respectively. The work function of the metal is

• A. 2h × 10¹4J
• B. 6h × 10¹4J
• C. 1.5h × 10¹4J
• D. 0.5h × 10¹4J

Hint:

In photoelectric effect: K.E. ∝ v² Always compare energies using velocity ratios.

Answer 1

The Correct Option is B

Step 1: Einstein photoelectric equation: hν - φ = (1)/(2)mv² Step 2: Given: (1)/(2)m(2v)² = 4((1)/(2)mv²) Step 3: Subtract equations: h(nu₂ - nu₁) = 3((1)/(2)mv²) ⟹ (1)/(2)mv² = (h(nu₂ - nu₁))/(3) Step 4: Work function: φ = hnu₁ - (h(nu₂ - nu₁))/(3) Using: nu₁ = fracc400nm, nu₂ = fracc250nm φ = 6h × 10¹4J