Question

The Rigel star flashes in a blue color whose wavelength is 400nm and the Betelgeuse star has a reddish color whose wavelength is 700nm. a) Estimate the surface temperature of rigel in degrees Kelvin. b) Estimate the surface temperature of Betelgeuse in Kelvin degrees. c) How many times is one of the stars colder than the other? which one is colder?

Answer 1

Wavelength and Temperature are related by Planck's blackbody radiation formula. This formula under certain assumptions reduces to Wein's formula which reads as follows:

lambda * T =2.898 x 10 ^-3 meter-kelvin (a constant) ( Wein's displacement law)

lambda has to be in meter unit.

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So, for Rigel T=2.898 x 10 ^-3 /(400*10^(-9) =  7245 K

for Betelgeuse, T= 2.898 x 10 ^-3 /(700*10^(-9) =4140    K

So, Betelgeuse is cooler. It is almost twice cooler than the other one.

Ratio is 4140/7245 = 0.57 approximately.