Surface Temperature of Stars in Orion Constellation

Question:

Based on the given data, what is the surface temperature of Betelgeuse, a red giant star, and Rigel, a bluish-white star in the constellation of Orion?

a) What is the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, which radiates with a peak wavelength of about 970 nm?

b) Rigel, a bluish-white star in Orion, radiates with a peak wavelength of 145 nm. Find the temperature of Rigel's surface.

Answer:

a) T = 2987.6 K

b) T = 19986.2 K

Answering the question above, the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, with a peak wavelength of about 970 nm is approximately 2990 K. On the other hand, Rigel, a bluish-white star in Orion, has a surface temperature of approximately 20,000 K.

Explanation:

The temperature of a star in terms of peak wavelength can be given by Wien's Displacement Law, which is as follows:

T = 0.2898 x 10^-2 m.K / λmax

Using the equation above, we can calculate the surface temperature of stars based on their peak wavelength:

a) For Betelgeuse with a peak wavelength of 970 nm:

T = 0.2898 x 10^-2 m.K / 9.7 x 10^-7 m = 2987.6 K

b) For Rigel with a peak wavelength of 145 nm:

T = 0.2898 x 10^-2 m.K / 1.45 x 10^-7 m = 19986.2 K

Therefore, Betelgeuse has a surface temperature of approximately 2990 K, while Rigel has a surface temperature of approximately 20,000 K.