Electricity and revolutions per second

[abeltyukov]

Hi,

Homework Statement

In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053 nm around a stationary proton. How many revolutions per second does the electron make?

Homework Equations

F = (kq1q2)/r^2 = (mv^2)/r

v = wr

The Attempt at a Solution

Charge of electron = -1.602 x 10^-19 C
Charge of proton = 1.602 x 10^-19 C
Mass of electron = 9.109 x 10^-31 kg

[(8.999 x 10^9)(1.602 x 10^-19)(1.602 x 10^-19)] / (0.053 x 10^-9) = (mv^2)/r

v = 0.002187 m/s

v = wr

0.002187 = w(0.053 x 10^-9)

w = 41267720.67


Any ideas on what I am doing wrong? Thanks!

 

[Kurdt]

You may find it easier to work algebraically until the last moment and then plug the numbers in. With the equations you have you want to rearrange of the angular speed (omega). Once you find omega you will then need to find the frequency. Do you know the equation to find the frequency?

 

[abeltyukov]

Can you give me an example please? Thanks!

 

[Kurdt]

Can you give me an example please? Thanks!

I'm not sure that would be constructive. The answer you get may look a little weird but that is because this is an exercise in showing how classical physics breaks down at the nano scale.

 

[BlazeSabre]

You forgot to square the radius below the charges. This changes the velocity to 2187190m/s. Then, in order to find rev/s you just divide the velocity by 2*pi*r giving a final answer of 6.568*10^15 rev/s.