The radius of circular electron orbits in the Bohr model of the hydrogen atom are given by (5.29 ✕ 10−11 m)n2, where n is the electron's energy level (see figure below). The speed of the electron in each energy level is (c/137n), where c = 3 ✕ 108 m/s is the speed of light in vacuum.

Question

(a) What is the centripetal acceleration of an electron in the ground state (n = 1)of the Bohr hydrogen atom?
magnitude( )m/s2
direction( )

(b) What are the magnitude and direction of the centripetal force acting on an electron in the ground state?
magnitude( )N
direction( )

(c) What are the magnitude and direction of the centripetal force acting on an electron in the
n = 2 excited state?
magnitude( )N

Answer 1

r = (5.29 ✕ 10−11 m)n^2

c = 3*10^8 m/s

v = 3*10^8/(137 n)

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1. if n = 1
Ac = v^2/r = 9*10^18/(18769*5.29*10^-11)
= 9.06*10^-5 * 10^18 * 10^11
= 9.06 * 10^24 m/s^2 yikes!
direction is toward the proton in the center of course :)
2. force = mass of electron * Ac

Now you should be able to do #3

Answer 2

An airplane starts from rest and accelerates at 11.5m/s2. What is its speed at the end of a 655m runway?

Answer 3

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