A typical galaxy has a mass of 10¹¹ M_ε. If 1% of this mass collects at the center of the galaxy to become a nonrotating black hole, what will be its Schwarzschild radius?

Question

Quizplus · Accepted Answer

The mass of the typical galaxy is given as $10^{11} M_{\odot}$, where $M_{\odot}$ is the mass of the Sun. If 1% of this mass becomes a black hole, the mass of the black hole would be $0.01 \times 10^{11} M_{\odot} = 10^9 M_{\odot}$. The Schwarzschild radius $R_s$ is given by $R_s = \frac{2GM}{c^2}$, where $G$ is the gravitational constant, $M$ is the mass of the black hole, and $c$ is the speed of light. Substituting the mass of the black hole and constants, the Schwarzschild radius for a $10^9 M_{\odot}$ black hole is approximately 20 astronomical units (au), making option A correct.

A Typical Galaxy Has a Mass of 1011 Mε

A Typical Galaxy Has a Mass of 10¹¹ M_ε