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Chapter 28: Problem 19

The magnetic character of bulk matter is determined largely by electron spin magnetic moments, rather than by orbital dipole moments. (Nuclear contributions are negligible, as the proton's spin magnetic moment is about 658 times smaller than that of the electron.) If the atoms or molecules of a substance have unpaired electron spins, the associated magnetic moments give rise to paramagnetic behavior or to ferromagnetic behavior if the interactions between atoms or molecules are strong enough to align them in domains. If the atoms or molecules have no net unpaired spins, then magnetic perturbations of the electron orbits give rise to diamagnetic behavior. a) Molecular hydrogen gas \(\left(\mathrm{H}_{2}\right)\) is weakly diamagnetic. What does this imply about the spins of the two electrons in the hydrogen molecule? b) What would you expect the magnetic behavior of atomic hydrogen gas (H) to be?

Short Answer

Expert verified
Answer: In H₂, weak diamagnetism implies that the two electrons have paired (opposite) spins, leading to no net unpaired electron spin and resulting in diamagnetic behavior. On the other hand, atomic hydrogen gas (H) is expected to exhibit paramagnetic behavior due to the presence of an unpaired electron spin.

Step by step solution

01

a) Implications of weak diamagnetism on electron spins in H₂

Molecular hydrogen gas (H₂) is weakly diamagnetic, which means the electrons in the molecule do not possess any net unpaired spins and the presence of an external magnetic field makes it repel slightly. In H₂, there are two electrons, and weak diamagnetism implies that these two electrons have paired (opposite) spins. When the spins are paired, their magnetic moments cancel each other out, leading to no net unpaired electron spin and resulting in diamagnetic behavior.
02

b) Predicting the magnetic behavior of atomic hydrogen gas (H)

Atomic hydrogen gas (H) has one electron in its outer shell. Since there is only one electron, it has an unpaired spin. An unpaired electron spin means that the magnetic moment is not canceled out, as there is no pairing with another electron. In such a scenario, the material exhibits paramagnetic behavior. Therefore, we can expect atomic hydrogen gas (H) to exhibit paramagnetic behavior due to the presence of an unpaired electron spin.

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Most popular questions from this chapter

Solenoid A has twice the diameter, three times the length, and four times the number of turns of solenoid B. The two solenoids have currents of equal magnitudes flowing through them. Find the ratio of the magnitude of the magnetic field in the interior of solenoid \(A\) to that of solenoid \(B\)

A long, straight wire lying along the \(x\) -axis carries a current, \(i\), flowing in the positive \(x\) -direction. A second long, straight wire lies along the \(y\) -axis and has a current \(i\) in the positive \(y\) -direction. What is the magnitude and the direction of the magnetic field at point \(z=b\) on the \(z\) -axis?

A hairpin configuration is formed of two semiinfinite straight wires that are \(2.00 \mathrm{~cm}\) apart and joined by a semicircular piece of wire (whose radius must be \(1.00 \mathrm{~cm}\) and whose center is at the origin of \(x y z\) -coordinates). The top straight wire is along the line \(y=1.00 \mathrm{~cm},\) and the bottom straight wire is along the line \(y=-1.00 \mathrm{~cm} ;\) these two wires are in the left side \((x<0)\) of the \(x y\) -plane. The current in the hairpin is \(3.00 \mathrm{~A},\) and it is directed toward the right in the top wire, clockwise around the semicircle, and to the left in the bottom wire. Find the magnetic field at the origin of the coordinate system.

28.39 The figure shows a cross section across the diameter of a long, solid, cylindrical conductor. The radius of the cylinder is \(R=10.0 \mathrm{~cm} .\) A current of \(1.35 \mathrm{~A}\) is uniformly distributed through the conductor and is flowing out of the page. Calculate the direction and the magnitude of the magnetic field at positions \(r_{\mathrm{a}}=0.0 \mathrm{~cm}\) \(r_{\mathrm{b}}=4.00 \mathrm{~cm}, r_{\mathrm{c}}=10.00 \mathrm{~cm}\) and \(r_{d}=16.0 \mathrm{~cm} .\)

Exposed to sufficiently high magnetic fields, materials saturate, or approach a maximum magnetization. Would you expect the saturation (maximum) magnetization of paramagnetic materials to be much less than, roughly the same as, or much greater than that of ferromagnetic materials? Explain why.
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