Chapter 11: Problem 3

Consider performing a Stern-Gerlach experiment on a beam of atoms that has two unpaired electrons. Would the magnetic moment be greater than, less than, or equal to the magnetic moment of \(\mathrm{H}\) ? Explain your reasoning.

Short Answer

Expert verified

The magnetic moment for atoms with two unpaired electrons would be greater than the magnetic moment of a hydrogen atom as each unpaired electron contributes equally to the magnetic moment, therefore doubling the total magnetic moment in comparison to \(\mathrm{H}\).

Step by step solution

Understand the Stern-Gerlach Experiment

The Stern-Gerlach experiment measures the quantization of angular momentum. In the simplest terms, it sends atoms through an inhomogeneous magnetic field and measures the resultant beam deflection due to the coupling of the magnetic moment of the atom with the magnetic field. For atoms with one unpaired electron, like hydrogen (\(\mathrm{H}\)), the deflection comes in two positions, signifying two quantization states of angular momentum.

Determine the Magnetic Moment for \(\mathrm{H}\)

The magnetic moment for a hydrogen atom is given by the formula \(\mu = g_s \cdot \frac{e \hbar}{2m_e}\), where \(g_s\) is the g-factor (approximately 2 for a free electron like in hydrogen), \(e\) is the charge of the electron, \(\hbar\) is the reduced Planck’s constant, and \(m_e\) is the electron's mass. This gives the magnetic moment for a single electron.

Compare the Magnetic Moment with Two Unpaired Electrons

Atoms with two unpaired electrons would have twice the deflection of hydrogen in the Stern-Gerlach experiment. This is due to the doubling of the total magnetic moment, as each unpaired electron contributes an equal amount. Therefore, the magnetic moment for atoms with two unpaired electrons would be greater than that of a hydrogen atom.

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Consider performing a Stern-Gerlach experiment on a beam of atoms that has two unpaired electrons. Would the magnetic moment be greater than, less than, or equal to the magnetic moment of \(\mathrm{H}\) ? Explain your reasoning.

Short Answer

Step by step solution

Understand the Stern-Gerlach Experiment

Determine the Magnetic Moment for \(\mathrm{H}\)

Compare the Magnetic Moment with Two Unpaired Electrons

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