Question

What is the Schwarzschild radius of a black hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.

a)1.2×10⁴m
b)2.4×10⁵m
c)2.4×10³m
d)1.2×10⁵m

Answer 1

The Schwarzschild radius of a black hole is a measure of the size of its event horizon. For a black hole with a mass eight times that of our Sun, the Schwarzschild radius is approximately 1.2 × 10^4 meters.

Step-by-step explanation:

The Schwarzschild radius of a black hole is a measure of the size of its event horizon, which is the boundary from which nothing can escape its gravitational pull, not even light. The formula for the Schwarzschild radius is given by:

Rs = 2GM/c^2

Where Rs is the Schwarzschild radius, G is the gravitational constant (6.67 × 10^-11 N·m²/kg²), M is the mass of the black hole, and c is the speed of light (3.00 × 10^8 m/s).

In this case, we have a black hole with a mass eight times that of our Sun. So, we can calculate the Schwarzschild radius as:

Rs = 2(6.67 × 10^-11)(8)(1.99 × 10^30) / (3.00 × 10^8)²

After evaluating this expression, we find that the Schwarzschild radius is approximately 1.2 × 10^4 meters.