Stars X and Y each radiate the same total power into space

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Stars X and Y each radiate the same total power into space. The radius of star Y is exactly one-half the radius of star X. What is the ratio

\lambda_Y/\lambda_X

of their peak-emission wavelengths, where

\lambda

denotes the wavelength at which each star’s emission is maximal? (a)

\sqrt2

(b)

\dfrac12

(c)

\dfrac1{\sqrt2}

(d) 1