An isolated conducting sphere of radius 9.0 cm is illuminated with monochromatic radiation of wavelength 310 nm. After sufficient time, photoelectric emission stops and the sphere carries a positive charge of 1.5×10⁻¹¹ C. Take hc = 1240 eV·nm and 1 ÷ (4πε₀) = 9×10⁹ N·m²·C⁻². If the threshold wavelength of the metal is N nm, find N.
Physics · Photoelectric effect and dual nature of matter · question based on photoelectric effect
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Question

An isolated conducting sphere of radius 9.0 cm is illuminated with monochromatic radiation of wavelength 310 nm. After sufficient time, photoelectric emission stops and the sphere carries a positive charge of 1.5×10⁻¹¹ C. Take hc = 1240 eV·nm and 1 ÷ (4πε₀) = 9×10⁹ N·m²·C⁻². If the threshold wavelength of the metal is N nm, find N.

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

G1 Physics · Accepted Answer

The final potential of the charged sphere is V = [1 ÷ (4πε₀)]Q ÷ R. Substitute: V = 9×10⁹×1.5×10⁻¹¹ ÷ 0.090 = 1.5 V. This is the stopping potential produced by self-charging, so the original maximum photoelectron kinetic energy was Kₘₐₓ = 1.5 eV. Photon energy at 310 nm: Eγ = 1240 ÷ 310 = 4.0 eV. Therefore the work function is φ = Eγ−Kₘₐₓ = 4.0−1.5 = 2.5 eV. Threshold wavelength: λ₀ = hc ÷ φ = 1240 ÷ 2.5 = 496 nm. Hence N = 496.