The variation of stopping potential (V₀) as a function of the frequency (v) of the incident light for a metal is shown in figure. The work function of the surface is

Solution

Physics sir · 4 steps

Read where the line cuts the frequency axis: that is ν₀, and hν₀ is the work function.

1. Einstein's equation. In terms of stopping potential, the photoelectric equation is eV₀ = hν - φ. So the graph of V₀ against ν is a straight line, and it reaches V₀ = 0 exactly when hν = φ.
2. Read the graph. The line meets the frequency axis at ν₀ = 5 × 10¹⁴ Hz. This is the threshold frequency, so the work function is φ = hν₀.

   φ = hν₀ = 6.63 × 10⁻³⁴ × 5 × 10¹⁴ = 3.315 × 10⁻¹⁹ J

3. Convert to eV. Divide by 1.6 × 10⁻¹⁹ J eV⁻¹: φ = (3.315 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) ≈ 2.07 eV.
4. So. The work function of the surface is 2.07 eV, option (d).

The idea to keep. On a V₀ against ν graph, the x-intercept is the threshold frequency, so φ = hν₀. The slope is always h/e, the same for every metal.

Answer from the NTA final answer key. Solution by PrepWiser.