What is the radius of an electron orbiting a proton with a 24-hour period?

[ahuebel]

I have this problem where we have to determine the radius between an electron orbiting a proton. It is assumed they attract each other with a 1/r^2 electric force. I assume this means they follow coloumb's law of k(q1*q2/r^2). The first part of the question asks...if the period of orbit is 24 hr, what is the radius.

At first I thought...gee an electron travels at the speed of light and it travels pi*d meters so solve for d and that is my answer. That is way to easy...So then I thought, perhaps I need to find this force of attraction as a function of r and then use that to find angular velocity and tangential acceleration and so on. Any ideas where to start on this one?

TIA

 

[LeonhardEuler]

An electron actually does not travel at the speed of light. It has a mass, and nothing with a mass can be accelerated to the speed of light. You don't know off the top of your head what the speed of an electron is, but your on the right track in the sense that if you did have the speed, you could find the radius by that method. How can you find the speed? I would guess that you are assuming a circular orbit, so you know that the acceleration is:
$$a=\frac{v^2}{r}$$
You don't know "a" yet. Can you think of a way to find it with some of the other information they gave you?

 

[ahuebel]

Well it is a circular orbit and I can calculate the force attraction between the two using coloumb's law but only as a function of r since I don't know the radius. And perhaps I use one of Newton's laws F=mv^2/r but I don't know if I Can really use a specific mass of an electron. Can I assume angular velocity omega = 2pi/T and then acceleration = omega^2*r. Similarly v = omega * r.

I am stumpped on the first two homework problems! This is not how I envisioned this semester starting :)

 

[LeonhardEuler]

You can find the mass of an electron on a table of constants. There is probably one in the front of your physics textbook. The mass is $9.109 \times 10^{-31}kg$. As for those angular equations you mentioned, they are valid and you can solve the problem with or without them.