A cooling object emits radiation of wavelength λ = 3000 + 40t Å, where t is in seconds. This radiation falls on a metal of work function 2 eV with constant incident power 100 W. The signal is ON for 2 min and OFF for 1 min, and each ON interval restarts at λ = 3000 Å. The metal is grounded, electron clouding is negligible, and photoemission efficiency is 0.01%. Find the maximum photocurrent in mA. Take hc = 12400 eV·Å.
Physics · Photoelectric effect and dual nature of matter
JEE Mains Advanced

Question

A cooling object emits radiation of wavelength λ = 3000 + 40t Å, where t is in seconds. This radiation falls on a metal of work function 2 eV with constant incident power 100 W. The signal is ON for 2 min and OFF for 1 min, and each ON interval restarts at λ = 3000 Å. The metal is grounded, electron clouding is negligible, and photoemission efficiency is 0.01%. Find the maximum photocurrent in mA. Take hc = 12400 eV·Å.

Physics · Photoelectric effect and dual nature of matter

G1 Physics · Accepted Answer

The photocurrent is I = eη(P/Eγ) = eηPλ/(hc), so it increases with λ while photoemission is possible. Threshold wavelength is λ₀ = hc/φ = 12400/2 = 6200 Å. The maximum occurs just before λ reaches 6200 Å. Substitution with η=10⁻⁴ and P=100 W gives Iₘₐₓ ≈ 5 mA.