# Electrical forces, application of Colomb's law

1. Jul 13, 2017

1. The problem statement, all variables and given/known data
"In an early attempt to understand atomic structure, Niels Bohr modeled the hydrogen atom as an electron in uniform circular motion about a proton with the centripetal force caused by Colomb attraction. He predicted the radius of the electron's orbit to be 5.29x10^(-11) m. Calculate the speed of the electron and the frequency of its circular motion.

2. Relevant equations

Fe = (kQq)/r^2
Fc = (mv^2)/r
Ac = (v^2)/r
3. The attempt at a solution

Honestly guys I this ones gonna take me a while so please work with me.

What I don't understand is:

Wouldn't they have to give us the velocity of the electron? Because there is a tangential acceleration and then radial acceleration.

So Colombs force is the centripetal force, $(kQq)/r^2 = (mv^2)/r$

$(kQq)/r = mv^2$

where k = 8.99 x 10^9, in this case proton has a charge of +e = 1.602 x 10^-19 C and electron has charge of -e = -1.602 x 10^-19 C, r = 5.29x10^11 m

so

$( (8.99 x 10^9)(1.602 x 10^{-19} C ) (-1.602 x 10^{-19} C ) ) / 5.29x10^{11} m = (mv^2)$

Does this seem right so far?

Now my concern is finding m. I'm not sure how to find the mass of an electron. The value is not given anywhere in my book... I'm really lost and this question is frustrating. If anyone can help I would appreciate it.

2. Jul 13, 2017

### TSny

You will need to look up the mass of the electron. If it's not in your textbook, check the web. Otherwise, your work looks good.

You might need to reconsider your signs. Left side of your last equation is negative while right side is positive.

(Typo: 5.29x10^11 m would be a pretty large atom.)

3. Jul 14, 2017

So would my answer be $\sqrt{(kQq)/(rm)} = v$ where k is constant Q is charge of proton q is charge of electron, r radius m mass??

?

Last edited: Jul 14, 2017
4. Jul 14, 2017

Yes.