A student measures stopping potentials for a metal: V₀ = 1.0 V at ν = 8.0 × 10¹⁴ Hz and V₀ = 2.24 V at ν = 1.1 × 10¹⁵ Hz. (a) Verify the linear law and estimate h. (b) Find the metal's work function. Solution: (a) Slope = ΔV₀/Δν = (2.24 − 1.0)/(1.1×10¹⁵ − 8.0×10¹⁴) = 1.24/(3.0×10¹⁴) ≈ 4.13×10⁻¹⁵ V·s. Since eV₀ = hν − φ, slope = h/e → h = e × slope = 1.6×10⁻¹⁹ × 4.13×10⁻¹⁵ ≈ 6.6×10⁻³⁴ J·s ✓ (matches Planck's constant). (b) φ = hν − eV₀ = (6.63×10⁻³⁴)(8.0×10¹⁴) − (1.6×10⁻¹⁹)(1.0) = 5.30×10⁻¹⁹ − 1.6×10⁻¹⁹ = 3.70×10⁻¹⁹ J ≈ 2.31 eV.