A black body has peak wavelength 6000 Å. Its temperature is increased so that its total radiated power becomes 16 times. The peak radiation at the new temperature falls on a metal. The stopping potential equals the excitation potential for the hydrogen transition n = 4 to n = 2. If the work function is α/100 eV, find α. Take hc = 12420 eV·Å.
Physics · Photoelectric effect and dual nature of matter
JEE Mains Advanced

Question

A black body has peak wavelength 6000 Å. Its temperature is increased so that its total radiated power becomes 16 times. The peak radiation at the new temperature falls on a metal. The stopping potential equals the excitation potential for the hydrogen transition n = 4 to n = 2. If the work function is α/100 eV, find α. Take hc = 12420 eV·Å.

Physics · Photoelectric effect and dual nature of matter

G1 Physics · Accepted Answer

Radiated power ∝T⁴, so a 16-fold increase means T doubles. By Wien's law, peak wavelength halves to 3000 Å, giving photon energy 12420/3000 ≈4.14 eV. The H transition 4→2 has excitation energy 13.6(1/4−1/16)=2.55 eV, equal to stopping potential energy. Thus φ≈4.14−2.55=1.59 eV=159/100 eV, so α=159.