1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mass of a black hole - given only the diameter

  1. Dec 3, 2011 #1
    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 [itex]1.0*10^{-15}[/itex], what would be the mass of a mini black hole?


    2. Relevant equations

    [itex]v=\sqrt{\frac{Gm}{r}}[/itex]


    3. The attempt at a solution

    [itex]v=\sqrt{\frac{Gm}{r}}[/itex]

    [itex]m=\frac{v^{2}r}{G}[/itex]

    [itex]m=\frac{(3.0*10^{8})^{2}(0.5*10^{-15})}{(6.67*10^{-11})}[/itex]

    [itex]m=6.75*10^{11} kg[/itex]

    It says that this is wrong, but I can't find my mistake. Thanks!
     
  2. jcsd
  3. Dec 3, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

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

    EDIT: D'Oh. No square root! Fixed it.
     
    Last edited: Dec 3, 2011
  4. Dec 3, 2011 #3
    Isn't the schwarzchild radius simply:

    [itex]R_s=\frac{2GM}{c^2}[/itex]

    So this would rearrange to

    [itex]m=\frac{rc^2}{2G}[/itex]

    and plugging in the values, I would get [itex]m=3.37*10^{11}kg[/itex]

    Is this now correct?
     
  5. Dec 3, 2011 #4

    gneill

    User Avatar

    Staff: Mentor

    Yes, and yes. Sorry about the square root distraction, I don't know where my head was at!
     
  6. Dec 3, 2011 #5
    Thanks for the help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook