Astrophysics physics alevel question.

Question: star x emits a wavelength of 480nm and has a luminosity of 4.1x10^26W.Astronomers deduce star X has a radius of 7x10^5km. A second star Y emits a peak wavelength of 450nm and has a luminosity of 4.8x10^26W. Calculate the radius of star Y.

The mark scheme uses luminosity equation to find the temperature of X and then uses proportionality (peak wavelength x T ) to determine temperature of Y.

I’m a bit confused on why we can’t just use peak wavelength= 1/T directly? It doesn’t give the right temperature answer but why?

Thanks for any help in advance.

Reply 1

Masad28

I believe it's because peak wavelength isn't equal to 1/T but it's proportional to it, meaning there is a constant involved in the formula. The constant being approximately 2.9*10^-3. So technically the formula would be peak wavelength = constant/T.

I hope this helped a bit if there's something you don't understand I'll try my best to clarify further.