The two stars have surface temperatures of 10,000K and 50,000K and the same radii. Which star will be brighter in the red

The two stars have surface temperatures of 10,000K and 50,000K and the same radii. Which star will be brighter in the red region of the spectrum (7000 angstroms) and how many times?

As is known, the higher the temperature of a star, the shorter-wavelength region of the spectrum the maximum of its radiation is shifted. However, with equal radii of stars, a hotter star will emit more energy in all ranges of electromagnetic radiation, as it follows from Planck’s formula, just in the long-wave region the difference will be less. The wavelength of 7000 angstroms is much longer than the wavelength of the maximum emission for both stars, and in this (Rayleigh-Jeans) region of the spectrum, the star’s luminosity is proportional to R2T (and not R2T4, as for the total luminosity). Consequently, a hotter star will be 5 times brighter in these rays.

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