# Orbital/Spin angular momentum + magnetic quantum numbers

• youngfreedman
In summary, for a single electron atom in a 4f1 excited state, the orbital angular momentum quantum number is l=3, the spin quantum number is s=1/2, and the principal quantum number is n=4. However, the value of J cannot be 1, so it is unclear what the associated magnetic quantum numbers, ml and ms, would be.
youngfreedman

## Homework Statement

A single electron atom has the outer electron in a 4f1 excited state. Write down the orbital and spin angular momentum quantum numbers and the associated magnetic quantum numbers for this state.

## Homework Equations

I don't think there is any relevant equations. I think it comes purely from the fact it's in a 4f1 excited state.

## The Attempt at a Solution

I originally thought it was l=3 for the orbital angular momentum quantum number, as I read that's what it is for "f". However, I am thrown off by the fact it's 4f1.

Thank you.

The subscript "1" should be the ## J ## value, but ## J=1 ## is not possible. I believe the 4 is the principal quantum number ## n ##. Meanwhile you can always say ## s=1/2 ##. They are also asking what values ## m_l ## and ## m_s ## can have.

## 1. What is orbital angular momentum?

Orbital angular momentum is a property of a particle's motion around a central point, such as an atom's nucleus. It is a vector quantity that describes the magnitude and direction of the particle's rotational motion.

## 2. How is orbital angular momentum quantized?

Orbital angular momentum is quantized because particles can only have specific values of angular momentum, determined by the quantum number l. This quantization is a consequence of the wave-like properties of particles at the atomic scale.

## 3. What is the significance of the magnetic quantum number?

The magnetic quantum number, denoted by m, describes the orientation of the orbital angular momentum vector relative to a chosen axis. It determines the number of possible orientations a particle can have in a given orbital, and it is also used to label energy levels and subshells in the atomic structure.

## 4. How does the spin angular momentum differ from the orbital angular momentum?

Spin angular momentum is a property of a particle's intrinsic spin, which is not related to its motion. Unlike orbital angular momentum, spin has no classical analogue and is always quantized in half-integer values. Spin also contributes to an atom's overall angular momentum and can interact with external magnetic fields.

## 5. What is the relationship between the orbital and spin quantum numbers?

The orbital and spin quantum numbers, l and s, respectively, are used to label different states of an electron in an atom. Together, they determine the overall quantum state of the electron and can be used to predict its energy, angular momentum, and magnetic properties.

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