# First Bohr Radius - Quantum and Atomic Model

## Homework Statement

Suppose an electron was bound to a proton, as in the hydrogen atom, but by the gravitational force rather than by the electric force. What would be the radius of the first Bohr orbit?

## Homework Equations

r = h^2 / 4∏^2*mke^2

## The Attempt at a Solution

I'm not sure how to manipulate the above equation to account for gravitational force. Should I start by looking at that fact

F = ma
kZe^2/r^2 = mv^2/r

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ehild
Homework Helper
Replace the electric force by the gravitational one. What is the force of gravity between two masses? (It is the mass of the proton and the mass of the electron now).

ehild

Ah, so F = km1m2/r^2 ?

Which means...

F = ma
km1m2/r^2 = mv^2/r

ehild
Homework Helper
"k" must be the gravitational constant, usually denoted by G.
So what do you get for r?

ehild

r = Gmm/mv^2

The question I now have is which mass will cancel as I have a mass in the numerator and denominator...

ehild
Homework Helper
Which particle orbits around the other?

ehild

The electrons orbit around the protons so does this mean the electron mass will cancel out?

ehild
Homework Helper
The electrons orbit around the protons so does this mean the electron mass will cancel out?
It needs the centripetal force, so the term mv^2/r refers to the
electron.

ehild