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Chapter 20: Problem 4

(a) Explain the two sources of magnetic moments for electrons. (b) Do all electrons have a net magnetic moment? Why or why not? (c) Do all atoms have a net magnetic moment? Why or why not?

Short Answer

Expert verified
Answer: The two sources of magnetic moments for electrons are the orbital magnetic moment (due to the motion of the electron in the orbit around the nucleus) and the spin magnetic moment (due to the intrinsic property of electrons called "spin"). Not all electrons have a net magnetic moment, as some can cancel each other out. Similarly, not all atoms have a net magnetic moment, as the combined magnetic moments of their electrons may also cancel each other out.

Step by step solution

01

Two sources of magnetic moments for electrons

The two sources of magnetic moments for electrons are the following: 1. Orbital magnetic moment: This magnetic moment is due to the motion of the electron in the orbit around the nucleus. When an electron orbits the nucleus, it creates a current loop, which generates a magnetic field and contributes to the overall magnetic moment of the electron. 2. Spin magnetic moment: This magnetic moment arises from the intrinsic property of electrons called "spin." Electrons have a quantum mechanical property called spin angular momentum, which gives rise to a magnetic moment. The spin magnetic moment is quantized and can only take two possible values in the presence of an external magnetic field.
02

Determine if all electrons have a net magnetic moment

Not all electrons have a net magnetic moment. The total magnetic moment of an electron depends on the vector sum of its orbital magnetic moment and spin magnetic moment. In some cases, these two magnetic moments can cancel each other out, resulting in a net magnetic moment of zero for the electron. This typically occurs in electron pairs with opposite spins, where the spin magnetic moments cancel each other.
03

Explain why not all electrons have a net magnetic moment

The reason not all electrons have a net magnetic moment is due to the way the magnetic moments interact. When electrons are paired in an orbital with opposite spins, their spin magnetic moments have equal magnitudes but opposite directions, causing them to cancel each other out. Additionally, when electrons completely fill an orbital subshell, their orbital magnetic moments also cancel each other out due to their symmetrical arrangement.
04

Determine if all atoms have a net magnetic moment

Not all atoms have a net magnetic moment. An atom's net magnetic moment depends on the combined magnetic moments of its electrons. If all the electrons in an atom have their magnetic moments paired and canceled out, the atom will have a net magnetic moment of zero. This is often the case for atoms with completely filled electron shells, which are usually found in the group of noble gases.
05

Explain why not all atoms have a net magnetic moment

The reason not all atoms have a net magnetic moment is that the magnetic moments of their electrons may cancel each other out when electron pairs have opposite spins or when electrons are arranged symmetrically in completely filled shells. Atoms with unpaired electrons, like those with incomplete electron shells, tend to have nonzero net magnetic moments, and they are called paramagnetic. In contrast, atoms with no net magnetic moment due to the cancellation of electron magnetic moments are called diamagnetic.

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Most popular questions from this chapter

Briefly explain why the magnitude of the saturation magnetization decreases with increasing temperature for ferromagnetic materials, and why ferromagnetic behavior ceases above the Curie temperature.

An iron bar magnet having a coercivity of \(7000 \mathrm{A} / \mathrm{m}\) is to be demagnetized. If the bar is inserted within a cylindrical wire coil \(0.25 \mathrm{m}\) long and having 150 turns, what electric current is required to generate the necessary magnetic field?

Cite the differences between type I and type II superconductors.

Briefly describe the phenomenon of magnetic hysteresis, and why it occurs for ferromagnetic and ferrimagnetic materials.

Compute (a) the saturation magnetization and (b) the saturation flux density for iron, which has a net magnetic moment per atom of 2.2 Bohr magnetons and a density of \(7.87 \mathrm{g} / \mathrm{cm}^{3}\).
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