Bohr Hypothesis: Proving Orbital Radius is Quantized

[Jason Gomez]

Homework Statement

Question:
If we assume that an electron is bound to the nucleus (assume a H atom) in a circular orbit, then the Coulomb force is equal to the centripetal force:
mv^2/r= ke^2/r^2
In the Bohr hypothesis, angular momentum, L = mvr is quantized as integer multiples of (h-bar): L = n(h-bar). Show that if this is true, orbital radius is also quantized: r = n^2aB.
aB = (hbar)^2/(ke^2m(electron))

Homework Equations

I have to be honest, I am completely lost. The book doesn't go in any detail and nor did the professor so I am stuck. If I could just get a helpfull hint or advice it would be greatly appreciated

The Attempt at a Solution

 

[kreil]

$$\frac{mv^2}{r} = \frac{ke^2}{r^2} \implies r = \frac{ke^2}{mv^2}$$

$$L = mvr = nh \implies r = \frac{nh}{mv}$$

If you combine these expressions and solve for the quantity (mv), you can then plug this back into solve for r:

$$\frac{ke^2}{mv^2} = \frac{nh}{mv}$$

 

[Jason Gomez]

Oh, let me work with that a little, I will be back on later, thank you

 

[Jason Gomez]

I forgot to come back because I have been busy, but thank you, that did help I figured it out.