USAAAO 2024, I кръг — Задача 23

• B

  The question is printed as VOIDED; the official solutions still give answer B.

Solution:

The luminosity $L$ of a star in terms of its radius $R$ and temperature $T$ can be written using Stefan-Boltzmann’s Law:

$\frac{L}{(R^2T^4)}$ is constant, and we know that the luminosity and radius of Recentus are $L_R = 4L_{\odot}$ and $R_R = 4R_{\odot}$:

Using Wein’s law, the peak emission wavelength of this star is $\lambda_R = \lambda_{\odot}\sqrt{2} \approx 710$ nm and the corresponding peak emission frequency is $4.2 \times 10^{14}$ Hz. Note that $\lambda_{\odot} = 502$ nm can be calculated from Wein’s constant and $T_{\odot}$ which are in the TOC.

Answer: B