Final answer:
The luminosity of a star can be calculated using the formula involving the star's radius and surface temperature. Given the star's radius as 3.5 Solar radii and temperature of 20,000 K, it will be much brighter than the Sun. The absolute magnitude can then be calculated from the luminosity and will be brighter than the Sun's.
Step-by-step explanation:
To calculate the luminosity of a star, you can use the formula L = 4πR²σT´, where L is the luminosity, R is the radius of the star, T is the surface temperature, and σ is the Stefan-Boltzmann constant (approximately 5.67 x 10⁻¸ W/m²·K´). Given that the star in question has a radius of 3.5 Solar radii (Rs) and a surface temperature of 20,000 K, we first need to convert the radius into meters using the solar raius which is approximately 6.96 x 10⁸ meters. The radius of the star, therefore, is 3.5 x 6.96 x 10⁸ meters. Plugging these values into the equation, we can calculate the luminosity. After getting the luminosity, the absolute magnitude can be calculated using the formula that relates the luminosity of a star to the Sun's luminosity and absolute magnitude (which is around 4.83 for the Sun).
However, without diving into the complex calculations, these values indicate that this star has a significantly larger radius and higher temperature compared to the Sun, thus it will have a much higher luminosity and a brighter absolute magnitude. Comparing the temperature and luminosity to the Sun suggests that this is no ordinary star but one that is quite extraordinary in its physical properties.