The centripetal force acting on the electron, allowing it to maintain its circular orbit around the nucleus, is
Here, we are asked to calculate the ’sum’ of the centripetal forces on an electron in a circular orbit of ‘presumed’ radius
For this problem, we can assume a simple model for the hydrogen atom that involves one particle (the electron) traveling in a circular orbit around another more massive particle (the hydrogen nucleus)...much like the moon orbits the earth!
If this is the case, the centripetal force can then be described by equation 1
or equation 2)
In equation 2,
At this point, finding the amount the centripetal force simply requires substituting the numerical values for the physical quantities
But before we do that, let’s make sure that the units of the physical quantities
Ultimately, in the end, we want a force in newtons, N.
The angular velocity of the electron,
...but we want
So let’s convert
So now, that our units are consistent, substituting