Chapter 26: Problem 24

Discuss quenching of orbital momentum in detail.

Short Answer

Expert verified

Quenching of orbital momentum happens when the total orbital angular momentum of a filled electron shell is zero due to specific spatial arrangement of the electrons. This leads to the total magnetic moment being purely due to the spin angular momentum of the electrons, giving evidence to the quantum mechanical nature of these quantities.

Step by step solution

Defining Orbital and Spin Moment

Orbital angular momentum relates to the motion of a particle around the nucleus of an atom, represented by the quantum number \(l\) ('ell'). It can be thought of as an analogue of classical angular momentum. Spin angular momentum, on the other hand, is a form of intrinsic angular momentum carried by the particle itself. It is quantified by the quantum number \(s\), and does not have an exact classical analogue.

The Quantum Mechanical Connection

In quantum mechanics, particles such as electrons in an atom possess both kinds of angular momentum at the same time. However, according to laws of quantum mechanics, only the combined total angular momentum is measurable rather than individual orbital or spin angular momentum.

Introducing Quenching of Orbital Momentum

In certain cases like the ground state for atoms with a filled electron shell, due to the very specific spatial arrangement of these electrons, the total orbital angular momentum of this shell becomes zero. This effect is termed as the quenching of orbital angular momentum. It happens due to the spatial symmetry of the electronic configuration.

Impact of Quenching to the Magnetic Moment

When orbital angular momentum is 'quenched' or made zero, the net magnetic moment of the atom becomes purely due to the spin angular momentum of the electrons. This leads to a deviation from the simple sum of the individual magnetic moments, which could be expected from a classical point of view, hence, showcasing the quantum nature of these quantities.

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Discuss quenching of orbital momentum in detail.

Short Answer

Step by step solution

Defining Orbital and Spin Moment

The Quantum Mechanical Connection

Introducing Quenching of Orbital Momentum

Impact of Quenching to the Magnetic Moment

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