Question

The peak intensity of radiation from a star named Sigma is 2 x 106 nm. What is the average surface temperature of Sigma rounded to the nearest whole number?

Answer 1

This is the classical thermo/ UV catastrophe thing that Planck solved for BB's. So we're looking at the peak temp for the given wavelength.

So try Wien's law? Means we can simplify by saying that:

\(\lambda_{max}=\dfrac{ b }{ T}\)


T in kelvins.

b, Wien's constant, is \(b \approx 2.9 \times 10^ {- 3} ~ m \cdot K\).

Sorting out the units:

\(T ={ 2.9 \times 10^{-3} \over 2 \times 10^6 \times 10^{-9} } \approx 1.45 ~ K\).

Quite chilly :)