Neon is a noble element and therefore forms a gas of...

Neon is a noble element and therefore forms a gas of monotomic molecules at all but the lowest temperatures. However, neon freezes and forms a crystalline solid at temperatures below $T=26 \mathrm{~K}$. Classically, how many degrees of freedom are in (a) a mole of neon gas at room temperature? (b) A mole of solid neon at $T=10 \mathrm{~K}$ ?

Key Concepts

Degrees of Freedom

Degrees of freedom refer to the number of independent ways in which a system can store or exchange energy. In the context of thermodynamics and statistical mechanics, each quadratic independent term in the energy (such as kinetic or potential energy) contributes one degree of freedom. The concept is crucial in determining how energy is partitioned among the different motions (translational, rotational, vibrational) of a system's constituent particles.

Monatomic Gas

A monatomic gas consists of individual atoms that are not bonded to each other, meaning that each atom only has translational motion in three dimensions. Since there are no bonds or internal structure, there are no rotational or vibrational degrees of freedom. This simplification leads to only three degrees of freedom per atom in the gas phase.

Vibrational Degrees of Freedom in a Solid

In a solid crystalline lattice, atoms are typically bound in place by potentials that allow them to vibrate about their equilibrium positions. Classically, each atom in a three-dimensional harmonic oscillator model has three degrees of freedom associated with kinetic energy and an additional three associated with potential energy, leading to a total of six degrees of freedom per atom. This concept is essential when assessing how energy is stored in the vibrations of a crystalline solid at a given temperature.

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