<span>In the Bohr model we assume that angular momentum is quantised:
L = mvr = nâ„Ź
From this you can find the expression for the tangential velocity of the electron. You then need to find the expression for the Bohr radius for a particular value of n, which turns out to be (for Z = 1, for Hydrogen-like atoms just replace e^2 with Z(e^2)):
rn=4πϵ0ℏ2n2/me2
When you sub in for r you get:
vn=e2/4πϵ0ℏ
From this you should be able to work out what the fine structure constant is - just compare the equation you were given to the one above. In undergrad physics courses the name "fine structure constant" is often applied to a few dimensionless constants that all look similar. It's just a number that happens to arise in a lot of Quantum Mechanical situations.</span>
