# Working out magnetic moment and electric quadrupole moment

• Flucky
In summary, the conversation discusses drawing the shell filling for oxygen isotopes and predicting their nuclear spin, parity, magnetic moment, and electric quadrupole moment. The values for these properties are determined for the isotopes 16O, 17O, and 18O, including the effects of valence neutrons and closed shells. There is some uncertainty about the contribution of neutrons to the electric quadrupole moment, but it is concluded that Q will be 0 for all oxygen isotopes due to the only change being in neutron number.
Flucky
Could somebody check if I have done this correctly please?

1. Homework Statement

Draw the shell filling for oxygen isotopes and make predictions of their nuclear spin, parity, magnetic moment and electric quadrupole moment.

## Homework Equations

Magnetic moment μ = gj j μN
Electric quadrupole moment Q ≈ -<r2>$\frac{2j - 1}{2(j + 1)}$

## The Attempt at a Solution

So starting off with the isotopes of oxygen: 16O, 17O, 18O16O
This fills the 1p$\frac{1}{2}$ shell.

spin = 0 because it is even-even
parity = 1 because even-even
μ = 0 because even-even
Q = 0 because it is a closed shell18O
This corresponds to the 1d$\frac{5}{2}$ shell.

Same values as above except for the electric quadrupole moment:

Q ≈ -<r2>$\frac{2(0) - 1}{2((0) + 1)}$ = -<r2>$\frac{-1}{2}$ = $\frac{1}{2}$<r2>17O
This corresponds to a valence neutron in the 1d$\frac{5}{2}$ shell.

spin = j = $\frac{5}{2}$
parity = (-1)l = (-1)2 = 1

μ = $\frac{5}{2}$ gj μN (I won't work out gj or put the value of μN in)

Q ≈ -<r2>$\frac{2(\frac{5}{2}) - 1}{2((\frac{5}{2}) + 1)}$ = -$\frac{4}{7}$<r2>

I think I may be wrong about the electric quadrupole moments, it's possible that only protons contribute to Q. So because the only thing that changes with oxygen isotopes is neutron number Q will be 0 for all of them?

EDIT: scratch that neutrons do actually contribute as they attract the protons slightly.

Last edited:

## 1. What is a magnetic moment and electric quadrupole moment?

A magnetic moment is a measure of the strength and direction of a magnetic field created by a charged particle or a current. It is a vector quantity and is usually expressed in units of ampere-meter squared (A•m^2). An electric quadrupole moment is a measure of the asymmetry in the distribution of electric charge within a system. It is a tensor quantity and is usually expressed in units of coulomb-meter squared (C•m^2).

## 2. How are magnetic moment and electric quadrupole moment related?

Magnetic moment and electric quadrupole moment are both related to the distribution of charge within a system. The magnetic moment is determined by the motion of charged particles, while the electric quadrupole moment is determined by the asymmetry in the distribution of charge. Both quantities are important for understanding the behavior of electrons and atoms in magnetic and electric fields.

## 3. How can magnetic moment and electric quadrupole moment be measured?

Magnetic moment and electric quadrupole moment can be measured using various experimental techniques such as nuclear magnetic resonance (NMR), electron spin resonance (ESR), and atomic force microscopy (AFM). These techniques involve applying an external magnetic or electric field and measuring the response of the system.

## 4. What factors affect the magnitude of magnetic moment and electric quadrupole moment?

The magnitude of magnetic moment and electric quadrupole moment is affected by the strength of the external magnetic or electric field, the distance between the charged particles within the system, and the orientation of the system with respect to the field. In addition, the properties of the particles themselves, such as their mass and charge, can also affect the magnitude of these moments.

## 5. Why are magnetic moment and electric quadrupole moment important in scientific research?

Magnetic moment and electric quadrupole moment are important in scientific research because they provide insight into the behavior of charged particles and atoms in the presence of external fields. These moments are crucial for understanding phenomena such as magnetism, chemical bonding, and the behavior of materials under different conditions. They also have practical applications in areas such as medical imaging, materials science, and quantum computing.

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