Stars A and B have the same radius, but the spectrum of star A peaks at a wavelength of 500 nm, whereas star B's spectrum peaks at 1000 nm. What is the ratio of the luminosity of star A to the luminosity of star B?
A) 1/16
B) 1/4
C) 4
D) 16

Question

Quizplus · Accepted Answer

The luminosity of a star can be determined using the Stefan-Boltzmann law, which states that the luminosity (L) is proportional to the fourth power of the star's temperature (T), L ∝ T^4. According to Wien's displacement law, the peak wavelength (λ_max) is inversely proportional to the temperature, λ_max ∝ 1/T. Therefore, if star A's spectrum peaks at a wavelength half that of star B (500 nm vs. 1000 nm), star A is twice as hot as star B. Since luminosity is proportional to the fourth power of the temperature, the luminosity of star A is 2^4 = 16 times that of star B.

Stars a and B Have the Same Radius, but the Spectrum