Question

The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume that the emissivity e is equal to 1 for these surfaces.

A) Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×10³¹W and has a surface temperature of 11,000 K. Assume that the star is spherical. Use σ=5.67×10−⁸ W/m₂⋅K₄ for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.

Answer 1

To find the radius of the star Rigel, we can use the Stefan-Boltzmann law and the given values of energy flux and temperature. Plugging in the values, we find that the radius of Rigel is approximately 5.1 x 10^8 meters.

Step-by-step explanation:

To find the radius of the star Rigel, we first need to use the Stefan-Boltzmann law which states that the energy flux from a blackbody is proportional to the fourth power of its absolute temperature. The equation for energy flux is F = σT^4, where F is the energy flux, σ is the Stefan-Boltzmann constant, and T is the absolute temperature of the star. Rearranging the equation, we get T = (F/σ)^(1/4). Plugging in the values for Rigel, we have T = (2.7x10^31W / (5.67x10^-8W/m^2⋅K^4))^(1/4) = 11062.36 K. Now, using the equation for energy flux F = 6T^4, we can solve for the radius Rigel: Rigel = (2.7x10^31W / (6 x (5.67x10^-8W/m^2⋅K^4) x (11062.36 K)^4))^(1/2) = 5.11 x 10^8 meters, which can be rounded to 5.1 x 10^8 meters.