# Why an atom can have nonzero toal angular momentum in the ground state?

• wdlang
In summary, an atom in its ground state has no net electric dipole momentum, but it is possible for it to have a nonzero angular momentum. This is not a spontaneous symmetry breaking, as a classical, charged, rotating ring can also have nonzero angular momentum without a dipole moment. In quantum mechanics, there are orbitals with angular momentum, and if there is a single electron in one of those orbitals, the total angular momentum will be nonzero. Intuitively, it may seem that a non-rotating state would have lower energy than a rotating one, but this is not always the case in quantum mechanics.

#### wdlang

In its ground state, an atom has no net electric dipole momentum ,but it can have a nonzero angular momentum.

Is this a spontaneous symmetry breaking?

why the ground state is not of zero angular momentum?

A classical, charged, rotating ring has no dipole moment, but nonzero angular momentum.
Why do you expect something special to get the same in quantum mechanics? There are orbitals with angular momentum, and if there are is a single electron in one of those orbitals you get a nonzero total angular momentum.

mfb said:
A classical, charged, rotating ring has no dipole moment, but nonzero angular momentum.
Why do you expect that this is something special to get the same in quantum mechanics? There are orbitals with angular momentum, and if there are is a single electron in one of those orbitals you get a nonzero total angular momentum.

intuitively, a non-rotating state is lower in energy than a rotating one

Well, this is not true in quantum mechanics, at least not in general. And if the low-energy states with zero angular momentum are filled, electron have to use some with angular momentum.

## 1. Why can't an atom have zero total angular momentum in the ground state?

An atom cannot have zero total angular momentum in the ground state because of the laws of quantum mechanics. According to these laws, an atom's electrons must occupy different energy levels, and each energy level has a corresponding angular momentum. In the ground state, the electrons occupy the lowest energy levels, which have non-zero angular momentum values, resulting in a non-zero total angular momentum for the atom.

## 2. How does an atom's electronic configuration affect its total angular momentum?

An atom's electronic configuration, which refers to the arrangement of its electrons in different energy levels, directly affects its total angular momentum. The electrons' distribution in different energy levels determines the atom's overall angular momentum, with the ground state having the lowest possible value.

## 3. Can an atom's total angular momentum change in the ground state?

No, an atom's total angular momentum cannot change in the ground state. The ground state is the lowest energy state an atom can have, and any change in the angular momentum would require the electrons to move to higher energy levels, resulting in an excited state.

## 4. Why is it important for an atom to have nonzero total angular momentum in the ground state?

Having a nonzero total angular momentum in the ground state is crucial for an atom's stability. According to the principles of quantum mechanics, electrons with the same angular momentum cannot occupy the same energy level. Therefore, if an atom's total angular momentum is zero, the electrons would have the same angular momentum, resulting in an unstable configuration.

## 5. How does the concept of spin contribute to an atom's total angular momentum in the ground state?

The concept of spin, which refers to the intrinsic angular momentum of particles, plays a significant role in determining an atom's total angular momentum in the ground state. Electrons have a spin of ½, which adds to the atom's total angular momentum. This contributes to the overall stability of the atom and its ground state.