Question

In the Bohr model of the hydrogen atom, an electron (mass = 9.1μ10-31 kg) orbits a proton (mass =
1.67μ10-27 kg) at a distance of 5.3μ10-11 m. (a) What is the gravitational force exerted by the proton on the
electron? (b) If the electric force of attraction between the particles is 8.2μ10-8 N, how many revolutions per
second does the electron make? (c) What is the tangential velocity of the elctron?

Answer 1

a) It's calculated the same as in classical mechanics.\[F_{g}=G \frac{ M_{e}M _{p} }{ r ^{2} }\]

Answer 2

b) Assuming any other force is negligible\[F = m _{e}a,\] where a is the centripetal force that binds the atom in a circular orbit.
\[a = \frac{ v ^{2} }{ r }=\omega ^{2}r\]
\[\omega=\frac{ 2\pi }{ t }\]

Answer 3

c) Using the second equation from b), you can get v, which is the tangential velocity.

I hope I didn't screw anything up. D: