Is the Schwarzschild Radius of a Proton Really That Small?

[toto93]

1. Calculate the schwarzschild radius of a proton



2. R = (2MG)/c^2



3. I plugged in m= 1.67E-27, G=6.67E-11 and c=3E-8 and got out an answer of 2.5E-54. This seems ridiculously small, but I can't figure our if I'm doing something wrong or if it really is just that tiny. The next question has us compare it to the radius of a proton, 0.8fm, so I'm guessing my answer should be somewhere around that value. If someone could help figure out what's going on I'd be grateful, Thanks,

 

[TSny]

Hello, toto93. Welcome to PF.
Your calculation looks correct. You are asked to compare the result to the known radius of the proton. That doesn't necessarily mean that the two radii should be similar.

 

[toto93]

Okay, I didnt think there was anything wrong with the maths it just seemed to be a ridiculously tiny number. The next questions asks us to compare it to see the possibility of it being a black hole, so I just thought they would be reasonably close. I guess it makes sense to be far smaller because then at least not everything is made of black holes. Thanks

 

[tansic]

I just did the calculations and my answer came out as 7.427E-46. Did you check your calculations or did I miss a conversion at some point?

 

[toto93]

Just done the calculation again, I'm fairly sure I did the calculation right and I got the same answer. It might be a problem with units, not sure. I'm just going to go with 2.48E-54 and hope it's right, I can't see any problems with my calculation at least

 

[TSny]

You can check your answer here

 

[toto93]

Thanks, that's really helpful, at least I know I'm pretty much certainly right. Thanks again,

 

[tansic]

Ok, I guess I messed up on my units. Wouldn't be the first time. Sorry 'bout that!