Exploring Star Temperatures with Wien's Displacement Law

What are the surface temperatures of the red giant star Betelgeuse and the bluish-white star Rigel?

Let's dive into the fascinating world of star temperatures!

Calculating the Surface Temperatures of Betelgeuse and Rigel

According to Wien's Displacement Law, we can determine the surface temperatures of stars by analyzing their peak wavelengths of radiation.

Wien's Displacement Law states that the peak wavelength of black body radiation is inversely proportional to the absolute temperature of the object. The law can be represented by the equation λ_max * T = b, where λ_max is the peak wavelength, T is the temperature, and b is Wien's constant (b = 2.898 x 10^-3 m*K).

Calculations:

(a) For Betelgeuse: - Peak Wavelength (λ_max) = 970 nm = 970 x 10^-9 m - Using Wien's Displacement Law: T = b / λ_max = (2.898 x 10^-3 m*K) / (970 x 10^-9 m) = 2989 K

(b) For Rigel: - Peak Wavelength (λ_max) = 145 nm = 145 x 10^-9 m - Using Wien's Displacement Law: T = b / λ_max = (2.898 x 10^-3 m*K) / (145 x 10^-9 m) = 20000 K

Therefore, the surface temperature of Betelgeuse is around 2989 K, while Rigel's surface temperature is approximately 20000 K. It's incredible to see the vast differences in temperatures between these two stunning stars!

Interested in learning more about star temperatures and the wonders of the universe? Check out additional resources to expand your knowledge!