# What facts are being used in this atomic structure question?

I wish to understand how to solve this atomic structure question:

For the ground state, the electron in the H-atom has an angular momentum = $\hslash$ , according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true, because:

1. Bohr model gives incorrect values of angular momentum.
2. only one of these would have a minimum energy.
3. angular momentum must be in the direction of spin of electron.
4. electrons go around only in horizontal orbits.

Actually, we have been taught Bohr orbits a lot in class, with formulae for everything (atomic radius/electron orbital speed/various energy levels/etc.) and also basics of the quantum mechanical model. However, we didn't go into such a great depth of Bohr orbits as asked in the above question.

Specifically, I don't know of any reasonable arguments against points 1,2,3. Point 4 is evidently wrong based on the quantum mech model.

How do I develop any claim for/against the points 1,2,3? What are the facts involved here?

The only correct answer is #1.

In actuality, the ground state of the hydrogen atom has zero angular momentum.

Regarding #2 and #4, there is no preferred plane in which one point should orbit another point. By symmetry, they are all equivalent.

Regarding #3, there is no angular momentum in the ground state, and in a state whether there is angular momentum, it doesn't need to be in the same direction as the electron spin angular momentum.

• Thank you! Can you please add some detail as to why it has zero angular momentum? And why are points 2 and 3 wrong? – Gaurang Tandon Jan 16 '18 at 15:23
• Oh, I just noticed your elaboration (next time please comment if you update your answer :)) I understand your logic for point 2, 3 and 4. For why there is zero angular momentum, I came across an old answer by you (coincidence ;))? Does that answer also apply in this question? – Gaurang Tandon Jan 24 '18 at 1:27