Electrostatics + Circular Motion

Question

In a helium atom, two electrons orbit the nucleus that consists of 2 protons and 2 neutrons. If the atomic radius of helium is 3.1x10^-11 m, what is the average kinetic energy of the electrons? (Assume that electrons are diametrically opposite to each other at all times)

Answer 1

r = radius of He atom

e = proton charge = magnitude of electron charge

k = electric force constant

m = mass of an electron

 

If the electrons are diametrically opposed to each other all the time (which in reality they are not), then the magnitude of the centripetal force on one electron is

 

mv²/r = k(2e)e/r² - ke²/(2r)²

 

Kinetic energy is

 

mv²/2 = (r/2)(mv²/r) = (r/2)[k(2e)e/r² - ke²/(2r)²]

 

All you have to do now is simplify the expression on the right, plug in the numbers, and evaluate.  You can look up the values of the constants in your physics book.