The magnetic moment of the Earth is approximately 8.00 ×10^22 A ·m^2 . Imagine that the planetar

step 1 In part A of this problem, we're asked to find the total number N of unpaired electrons. And to

The magnetic moment of the Earth is approximately 8.00...

The magnetic moment of the Earth is approximately $8.00 \times 10^{22} \mathrm{A} \cdot \mathrm{m}^{2} .$ Imagine that the planetary magnetic field were caused by the complete magnetization of a huge iron deposit with density 7900 $\mathrm{kg} / \mathrm{m}^{3}$ and approximately 8.50 $\times 10^{28}$ iron atoms/m^{3} . (a) How many unpaired electrons, each with a magnetic moment of 9.27 $\times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2}$ , would participate? (b) At two unpaired electrons per iron atom, how many kilograms of iron would be present in the deposit?

Key Concepts

Magnetic Moment

Magnetic moment quantifies the strength and orientation of a magnetic source. In planetary physics, it describes how a planet like Earth interacts with its surrounding magnetic field, and at the atomic level, it indicates the contribution from electrons. This concept is central to understanding both macroscopic magnetic effects and microscopic contributions from individual magnetic dipoles.

Atomic Magnetic Moment

The atomic magnetic moment arises primarily from the spin and orbital motion of electrons within atoms. Unpaired electrons, each possessing a specific magnetic moment, contribute to an atom’s net magnetism. This idea is crucial when considering how many atomic-scale dipoles are required to produce a given macroscopic magnetic moment.

Unpaired Electrons

Unpaired electrons are electrons that do not have a partner with opposite spin in their orbital, making them significant contributors to a material’s magnetic properties. Their magnetic moments add together in substances like iron, leading to the overall magnetization witnessed in ferromagnetic materials.

Magnetization

Magnetization is the process or degree to which a material becomes magnetically active, expressed as the magnetic moment per unit volume. It connects the microscopic contributions from individual atoms or electrons to the bulk magnetic properties of a material, such as a large iron deposit.

Material Density and Atomic Number Density

Material density provides a measure of mass per unit volume, while atomic number density specifies how many atoms exist per unit volume. These concepts are key in relating macroscopic properties of materials to the number of contributing atomic-scale magnetic dipoles and in estimating the total mass or number of unpaired electrons required to achieve a certain magnetic effect.

Transcript

Please give Ace some feedback