Light of wavelength 3540 Å falls on a metal of work function 2.5 eV. The emitted electrons, at 10¹⁸ electrons per second, transfer their entire maximum kinetic energy as heat to a target metal of mass 10⁻³ kg and specific heat 160 J kg⁻¹ °C⁻¹. Find the rate of temperature rise in °C s⁻¹. Take hc = 12400 eV·Å.
Physics · Photoelectric effect and dual nature of matter
JEE Mains Advanced

Question

Light of wavelength 3540 Å falls on a metal of work function 2.5 eV. The emitted electrons, at 10¹⁸ electrons per second, transfer their entire maximum kinetic energy as heat to a target metal of mass 10⁻³ kg and specific heat 160 J kg⁻¹ °C⁻¹. Find the rate of temperature rise in °C s⁻¹. Take hc = 12400 eV·Å.

Physics · Photoelectric effect and dual nature of matter

G1 Physics · Accepted Answer

Step 1: Photon energy is 12400/3540 ≈ 3.50 eV, so Kₘₐₓ ≈ 1.00 eV. Step 2: At 10¹⁸ electrons s⁻¹, heating power ≈ 1.00×10¹⁸×1.6×10⁻¹⁹ = 0.16 W. Since mc = 10⁻³×160 = 0.16 J °C⁻¹, rate of temperature rise ≈ 1 °C s⁻¹.