The work functions of Aluminium and Gold are 4.1 eV and and 5.1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

Solution

Physics sir · 4 steps

Write Einstein's equation for stopping potential: the slope is h/e, and the metal never enters it.

1. Einstein's equation. The fastest photoelectron has kinetic energy hν - φ₀, and the stopping potential V₀ stops it exactly, so eV₀ = hν - φ₀.

   V₀ = h/e ν - φ₀/e

2. Read the graph. This is a straight line in ν. The slope is h/e, built only from universal constants. The work function φ₀ sits only in the intercept, so it shifts the line without tilting it.
3. Compare the metals. Gold and aluminium give parallel lines, both with slope h/e ≈ 4.14 × 10⁻¹⁵ V s. Only the threshold frequencies differ.
4. So. The ratio of the slopes is (h/e)/(h/e) = 1, option (c).

The idea to keep. On a V₀ versus ν graph, the slope is always h/e for every metal. The work function only decides where the line cuts the axes, so the lines for different metals are parallel.

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