# Homework Help: Mass of a black hole - given only the diameter

1. Dec 3, 2011

### PirateFan308

1. The problem statement, all variables and given/known data
Cosmologists have speculated that black holes the size of a proton could have formed during the early days of the Big Bang when the universe began. If we take the diameter of a proton to be $1.0*10^{-15}$, what would be the mass of a mini black hole?

2. Relevant equations

$v=\sqrt{\frac{Gm}{r}}$

3. The attempt at a solution

$v=\sqrt{\frac{Gm}{r}}$

$m=\frac{v^{2}r}{G}$

$m=\frac{(3.0*10^{8})^{2}(0.5*10^{-15})}{(6.67*10^{-11})}$

$m=6.75*10^{11} kg$

It says that this is wrong, but I can't find my mistake. Thanks!

2. Dec 3, 2011

### Staff: Mentor

The Schwarzchild radius is given by:
$$r_s = \frac{2 G M}{c^2}$$
I think you forgot the factor of 2.

EDIT: D'Oh. No square root! Fixed it.

Last edited: Dec 3, 2011
3. Dec 3, 2011

### PirateFan308

$R_s=\frac{2GM}{c^2}$

So this would rearrange to

$m=\frac{rc^2}{2G}$

and plugging in the values, I would get $m=3.37*10^{11}kg$

Is this now correct?

4. Dec 3, 2011

### Staff: Mentor

Yes, and yes. Sorry about the square root distraction, I don't know where my head was at!

5. Dec 3, 2011

### PirateFan308

Thanks for the help!