How Does the Event Horizon Size of a Black Hole Compare to Its Predecessor Star?

[bobo1455]

Here's the question:

One of the brightest stars in our night sky is a red supergiant with a mass about 10× the
Sun’s mass and a radius about 1000× the Sun’s radius. At the end of its life it will explode
as a supernova and then collapse and become a black hole. How large will the black hole’s
event horizon be compared to the size of the supergiant now.

The answer choices are given as multiple choice:

(A) 0× the supergiant’s radius
(B) 0.00000004× the supergiant’s radius
(C) 0.000004× the supergiant’s radius
(D) 0.0004× the supergiant’s radius
(E) 0.04× the supergiant’s radius

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My attempt:

I'm going to use formula for Schwarzschild radius which is: r = 2*G*m / c^2

The question said mass 10x the Sun's mass, so Sun's mass = 1.98 * 10^30 kg, the mass I'm using will be 10x that, which is: 1.98 * 10^31 kg

And then I plugged that into the formula and got: 14.7690207 km

Then, the question says that the radius of the Supergiant is 1000x that of the Sun's radius. I have the Sun's radius as: 695000 km, so 695000 * 1000 km is what I am using.

Finally, I take 14.7690207 km and divide it by 695,000,000 and get: 0.0000000212503895

The answer is closest to (B), but what I calculated is literally half of answer (B).

I figured, maybe the event horizon is like the diameter, so what I have is actually the ratio of the radius, so I should double it and that would give me (B), but I am not sure if that's right or not.

What am I missing here? Thanks in advance.

 

[phyzguy]

I think you forgot the factor of 2 in the r = 2Gm/c^2. A 10 solar mass black hole should have e Schwarzschild radius of about 30 km.

 

[bobo1455]

Oh yeah, you're right. Thanks!