In the Bohr theory of the hydrogen atom, an electron moves with constant speed i
ID: 2269701 • Letter: I
Question
In the Bohr theory of the hydrogen atom, an electron moves with constant speed in a circular orbit about a proton, where the radius of the orbit is 0.53 x 10-10 m.
a) Determine the electrostatic force (magnitude and direction) exerted by the proton on the electron.
b) Determine the electrostatic force (magnitude and direction) exerted by the electron on the proton.
c) If this force causes the centripetal acceleration of the electron, what is the speed of the electron? (The mass of the electron is m=9.11*10^-31 kg.)
Explanation / Answer
a)
Coulombs Law
F = k *q1 q2 / r^2
q_1 = charge of the electron, q_2 = charge of the proton, r = 0.53 x 10^-10 m
force= 8.20*10^-8 N
b) Coulomb's Law again, but this time you should put a minus in front of answer. The force is operating in the opposite direction.
f= -8.20*10^-8 N
c) Equate the answer from (a) to mv^2 / r. Rearrange for v.
v= 2.18*10^6 m/s