# Exploring Orbital Magnetic Moment through P-Orbitals and Quantum Physics

• johng23
In summary, The class discusses how for p-orbitals, the orbital angular momentum is zero when there are three electrons in the subshell, resulting in no orbital magnetic moment. However, if there are one or two empty p-orbitals, the angular momentum does not sum to zero, resulting in a net angular momentum and a magnetic moment. It is important to note that calling L a vector may be inaccurate, but it is still used in the context of this treatment. Furthermore, it is possible to determine which orbitals are occupied by one or two electrons in the p subshell, which can explain the inconsistency in the argument.
johng23
I am taking a class which discusses orbital angular momentum in a pseudo-quantum way, and it was explained that the orbital angular momentum is zero if the time average of the individual "L vectors" sum to zero. I am considering p-orbitals. The argument is that, if there are 3 electrons in the subshell, the orbital angular momentum sums to zero and the atom has no orbital magnetic moment. The magnetic moment arises when there are one or two empty p-orbitals, in which case the angular momentum does not sum to zero.

Suppose I have one electron in the m=0 state, so that its "L vector" is in the x-y plane. The vector can take any orientation in the plane, so its time average is zero and there should be no net angular momentum by this argument, but of course that isn't true because the p-orbital does have angular momentum and the choice of axes is arbitrary. Also since the other p-orbitals are empty, there should be net angular momentum and thus a magnetic moment by the other argument from the class.

I have read that calling L a vector is inaccurate, but even if that is the case I would like to understand it as well as possible in the context of this treatment.

Just wondering if it's a hard question or if I'm explaining it poorly.

If i have one or two electrons in the p subshell, is it possible to know which orbitals they occupy? If it's not, then that could explain this. For one electron, if it's in the m=0 the angular momentum averages to zero, but you have to also consider the average angular momentum of the other indistinguishable cases. In that way, 1 electron or 2 electrons does not average to zero angular momentum, but 3 in the p-shell does.

## 1. What is an orbital magnetic moment?

An orbital magnetic moment is a property of an atom or molecule that arises from the motion of electrons around the nucleus. It is a measure of the strength and direction of the magnetic field produced by the orbital motion of electrons.

## 2. How are p-orbitals involved in exploring orbital magnetic moment?

P-orbitals are one of the three types of orbitals (along with s and d orbitals) that describe the spatial distribution of electrons around an atom's nucleus. They play a key role in determining the orbital magnetic moment because their shape and orientation allow for the maximum possible magnetic interaction between the electrons and the external magnetic field.

## 3. What is the relationship between orbital magnetic moment and quantum physics?

The concept of orbital magnetic moment is rooted in quantum physics, specifically in the principles of angular momentum and orbital magnetic dipole moment. Quantum mechanics provides the mathematical framework for understanding the behavior of electrons in atoms and molecules, and thus plays a crucial role in studying orbital magnetic moment.

## 4. How is exploring orbital magnetic moment useful in scientific research?

Understanding orbital magnetic moment is important not only for fundamental research in quantum physics, but also for practical applications such as magnetic resonance imaging (MRI) and magnetic data storage. By studying and manipulating the orbital magnetic moment, scientists can gain insights into the behavior of electrons and develop new technologies.

## 5. What techniques are commonly used to explore orbital magnetic moment?

Some common techniques used to study orbital magnetic moment include electron spin resonance (ESR), nuclear magnetic resonance (NMR), and Mössbauer spectroscopy. These methods involve applying external magnetic fields and measuring the resulting changes in the energy levels and transitions of electrons or nuclei, allowing for the determination of the orbital magnetic moment.

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