A metal of work function 2.0 eV is illuminated with monochromatic radiation of wavelength 200 nm. Take hc = 1240 eV·nm, mₑ = 9.1×10⁻³¹ kg and 1 eV = 1.6×10⁻¹⁹ J. If the maximum photoelectron speed is approximately N×10⁵ m·s⁻¹, find N to the nearest integer.
Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect
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Question

A metal of work function 2.0 eV is illuminated with monochromatic radiation of wavelength 200 nm. Take hc = 1240 eV·nm, mₑ = 9.1×10⁻³¹ kg and 1 eV = 1.6×10⁻¹⁹ J. If the maximum photoelectron speed is approximately N×10⁵ m·s⁻¹, find N to the nearest integer.

Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect

G1 Physics · Accepted Answer

Photon energy: Eγ = 1240 ÷ 200 = 6.20 eV. Maximum kinetic energy: Kₘₐₓ = Eγ−φ = 6.20−2.00 = 4.20 eV. Convert to joules: Kₘₐₓ = 4.20×1.6×10⁻¹⁹ = 6.72×10⁻¹⁹ J. Use Kₘₐₓ = (1 ÷ 2)mₑvₘₐₓ². Therefore, vₘₐₓ = √[2Kₘₐₓ ÷ mₑ] = √[(2×6.72×10⁻¹⁹) ÷ (9.1×10⁻³¹)] ≈ 1.22×10⁶ m·s⁻¹. Thus, vₘₐₓ ≈ 12.2×10⁵ m·s⁻¹. To the nearest integer, N = 12.