Conceptual question from Atomic Structure

[dreamz25]

It is well known that, "Neil bohr failed in his model in which he described an electron as a charged particle moving in well defined circular orbits about the nucleus." However he failed because of the two major reasons..
a) It didn't consider the wave nature of the electrons
b) contradicts the uncertainity principle (which is true for microscopic particles).
so if the orbits are not "properly defined", whey then do we use the formula for the electrons in the nth orbit of a Hydrogen atom like...
the energy of an electron in the nth orbit = -R_H (1/n²)
Radius of an electron in the nth orbit = a₀ n²
i mean "if the theory of existence of such well defined trajectories is meaningless" then why not the formulas?

 

[jtbell]

so if the orbits are not "properly defined", whey then do we use the formula for the electrons in the nth orbit of a Hydrogen atom like...
the energy of an electron in the nth orbit = -R_H (1/n²)

We can get the discrete energies for the electron in hydrogen by solving the Schrödinger equation for the hydrogen atom, without any reference to "electron orbits."

Radius of an electron in the nth orbit = a₀ n²

Nobody talks nowadays about the "radius of an electron orbit" except in a historical context when discussing Bohr's original theory.

 

[DrewD]

for a lot of quick calculations/estimates, Bohr's constants are fine, but they are not "conceptually" meaningful, if that makes sense. Especially in entry level classes before full QM is introduced, these formulas do come in handy, but now they are seen as artifacts of a deeper theory.