Consider an imaginary scenario, where a black hole has the size of a hydrogen atom.
What would be the mass of the black hole?
The Schwarzschild radius, r_s, is the radius of the event horizon for a given mass. So, a requisite amount of mass must be within this radius in order to have a blackhole.
r_s = 2 M G/ c^2
so:
M = (r_s) c^2 /(2 G}
We will take the "size" of the H atom to be the Bohr radius. That's the orbit of the ground state electron. (The only alternative would be to use the proton radius, but that would then be the "hydrogen ion size", or "nucleus size")
We'll work in mks: meters, kilograms, seconds.
r_s = 5.29 10^(-11) [m] Bohr radius
G = 6.6743 10^(-11) [N m^2 / (kg)^2] Univ gravitational const.
where N is Newtons. [kg m/s^2] mks unit of force
c = 2.9979 10^8 [m/s] speed of light
this gives:
M = 3.56 10^16 [kg]
For comparison, the 11 km radius Halley's Comet mass is 2 10^14 [kg]
Edited on December 8, 2022, 9:59 am
soln
