What is the radius of a red giant star that has a luminosity of 300 L _$\odot$ and a temperature of 4000 K? (Note that the temperature of the Sun is 5800 K.) A) 8 R _$\odot$ B) 13 R _$\odot$ C) 25 R _$\odot$ D) 36 R _$\odot$ E) 65 R _$\odot$

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Quizplus · Accepted Answer

The luminosity of a star is proportional to the square of its radius and the fourth power of its temperature. Using the formula L = 4πR²σT⁴, and comparing it to the Sun's values, we can solve for the radius. Given the luminosity is 300 times that of the Sun and the temperature is lower, the radius must be significantly larger. Calculating gives approximately 36 times the Sun's radius.

What Is the Radius of a Red Giant Star That ⊙\odot⊙

What Is the Radius of a Red Giant Star That $\odot$