Exploring Quantum Physics - Final Exam Part 2 Question 6

Question:

What is the required frequency stir an atom is a trap of 20 micron radius to put the an atom with in $L_3 = 1 \times \hbar$?

Solution:

Disclaimer - I have got this problem wrong - and there is no official solution yet, so this is at best a sharing of my idea.

The Bohr model gives $mvr = n\hbar$. The problem requires $n = 1$, so we got almost everything in this equation, except $v$ .

If a stirrer is operating at a certain frequency $f$, then a particle being stirred will have travelled a circle in one period of time, in other words, $v = \frac{d}{T} = \frac{2\pi r}{T} = 2\pi r f$.

Substitute this back to the equation we get

$m (2 \pi r f) r = \hbar$. So $f = \frac{\hbar}{2 \pi r^2 m} = \frac{h}{ r^2 m} = 43 Hz$

I didn't know what I pick $10^6 Hz$ at that point - perhaps I was just too nervous. I am not sure if the current answer is correct either. But that's the idea - the problem isn't too hard. It is just that the climax was just too high :p