Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted by B. Let λ₁ and λ₂ be the wavelengths of maximum intensity for stars A and B, respectively. Find λ₁/λ₂.
Physics · Thermodynamics
JEE Advanced 2015

Question

Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted by B. Let λ₁ and λ₂ be the wavelengths of maximum intensity for stars A and B, respectively. Find λ₁/λ₂.

Physics · Thermodynamics

JEE Advanced 2015

G1 Physics · Accepted Answer

For stars A and B, let R₁,R₂ be their radii, P₁,P₂ their powers and T₁,T₂ their temperatures. Stefan's law gives P∝R²T⁴. With R₁/R₂=400 and P₁/P₂=10⁴, we get T₁/T₂=1/2. By Wien's law λT=constant, λ₁/λ₂=T₂/T₁=2.