One star has a surface temperature of 6000 K and another has a surface temperature of 7000 K. If the two stars have the same absolute luminosity, and if the radius of the 6000 K star is R₆ and the radius of the 7000 K star is R₇, what is the ratio R₆/ R₇? A)0.7 B)1.2 C)1.4 D)1.6 E)1.9

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to the square of its radius and the fourth power of its temperature (L ∝ R²T⁴). Given that both stars have the same luminosity, we have R₆²(6000)⁴ = R₇²(7000)⁴. Solving for the ratio R₆/R₇ gives (7000/6000)² = (7/6)² = 1.4.

One Star Has a Surface Temperature of 6000 K and Another