Question

In the Bohr model of the hydrogen atom,
the speed of the electron is approximately
2.41 × 10^6 m/s.
Find the central force acting on the electron
as it revolves in a circular orbit of radius
5.15 × 10^−11 m. Answer in units of N.

Find the centripetal acceleration of the electron. Answer in units of m/s^2.

Answer 1

F = k q1 q2 / r^2
k = 9*10^9
q1 = -1.6 * 10^-19
q2 = +1.6 * 10^-19
R = 5.15*10^-11
SO
F = -9*10^9 * 1.6^2 * 10^-38 / 5.15^2*10^-22
=-.869*10^-7 N = -8.69*10^-8 N
negative r is inward direction

v^2/r = -(2.41)^2*10^12/5.15*10^-11
=-1.13*10^23
also acceleration inward toward center

rough check
does F = ma?
F = -8.69 * 10^-8
m a = 9.11*10^-31 *-1.13*10^23 = -10.3 *10^-8

off by about 15%. Not too bad for a rough estimate