Practice question
Question
The work function of a metal is \( 2.4 \, \text{eV} \). Light of wavelength \( 350 \, \text{nm} \) is
incident on it. What is the maximum speed of emitted electrons? (Take \( h c = 1240 \, \text{eV nm} \),
\( m_e = 9.11 \times 10^{-31} \, \text{kg} \))
Explanation
**Work function** Φ minimum energy to escape, for Φ=2.2 eV λ₀=1240/2.2=563.6 nm, Φ=3.0 eV threshold frequency f₀=Φ/h=3×1.6×10⁻¹⁹/6.63×10⁻³⁴=7.24×10¹⁴ Hz, stopping potential V₀ = (h f - Φ)/e, for 0.7 V K_max=0.7 eV, for 1.5 V K_max=1.5 eV, intensity increase increases photocurrent not K_max, frequency below threshold no emission regardless of intensity. E = (h c/λ) = (1240/350) ≈ 3.543 eV . Kₘₐₓ = E - Φ₀ = 3.543 - 2.4 = 1.143 eV = 1.143 × 1.6 × 10⁻¹⁹ = 1.8288 × 10⁻¹⁹ J . vₘₐₓ = √((2 Kₘₐₓ/m)) = √((2 × 1.8288 × 10⁻¹⁹/9.11 × 10⁻³¹)) ≈ 6.33 × 10⁵ m/s . Applying E =
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