Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat at the rate of 2.70 × 1030 W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10^-8 W/m² · K⁴. A) 7.80 × 10¹⁰ m B) 8.70 × 10¹⁰ m C) 1.40 × 10¹¹ m D) 1.90 × 10¹¹ m E) 2.16 × 10¹¹ m

Question

Quizplus · Accepted Answer

Using the Stefan-Boltzmann law, L = 4πR²σT⁴, we solve for R: R = √(L / (4πσT⁴)). Substituting L = 2.70 × 10³⁰ W, σ = 5.670 × 10⁻⁸ W/m²·K⁴, and T = 3000 K, we find R ≈ 2.16 × 10¹¹ m.

Betelgeuse Is a Red Supergiant Star in the Constellation Orion