Bohr's Model of the Atom: Correct Answers from an Incorrect Hypothesis?

[bon]

Homework Statement

In the Bohr atom, electrons move on classical circular orbits that have angular momenta lh/2pi,
where l = 1, 2, . . ..
Show that the radius of the first Bohr orbit is a0 and that the model predicts the
correct energy spectrum.

In fact the ground state of hydrogen has zero angular momentum. Why
did Bohr get correct answers from an incorrect hypothesis?

Homework Equations

The Attempt at a Solution

Ok so I've done the first part. I'm just not sure on the last question - why did bohr get correct answers from an incorrect hypothesis?

 

[jbsteele]

The radius of the first Bohr orbit is a0, which is equal to h/2πm(e)v. This is because angular momentum of the electron is given by lh/2π, and for the first Bohr orbit (l=1), the angular momentum is equal to h/2πm(e)v. This then gives us the equation for the radius of the first Bohr orbit, a0. For the energy spectrum, the energy of the electron in the nth orbit is given by E = -(m(e)e^4)/(2h^2n^2). This equation is correct and matches the correct energy spectrum for hydrogen. So why did Bohr get correct answers from an incorrect hypothesis? I'm not sure on this one. Can anyone help me out?