Chapter 42: Problem 8
Two atoms of cesium (Cs) can form a Cs \(_{2}\) molecule. The equilibrium distance between the nuclei in a \(\mathrm{Cs}_{2}\) molecule is \(0.447 \mathrm{nm} .\) Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is \(2.21 \times 10^{-25} \mathrm{~kg}\).
Short Answer
Step by step solution
Understanding the System
Convert Distance Units
Locate the Center of Mass
Use Moment of Inertia Formula
Plug in Values and Calculate I
Final Calculation
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Cs2 Molecule
The cesium molecule, Cs extsubscript{2}, is formed when two cesium atoms bond together. This bonding is typically due to the sharing of electrons, creating a covalent bond. The molecule has a linear configuration because both atoms are identical and equally attract the shared electrons.
Understanding molecules like Cs extsubscript{2} can help in studying properties such as molecular orbitals, bond lengths, and moment of inertia, as seen in the given exercise.
Cesium Atom
One unique property of cesium is its relatively large atomic mass and size compared to other alkali metals, which affects its physical and chemical behavior. The mass of the cesium atom is crucial in calculations involving molecular structures, such as determining the moment of inertia in the given exercise. This demonstrates how fundamental attributes of a cesium atom help determine the characteristics of larger structures like molecules.
Equilibrium Distance
This measurement signifies the average distance between the nuclei of the cesium atoms when they are bonded in the Cs extsubscript{2} molecule.
Equilibrium distance is crucial for understanding molecular geometry and properties such as bond strength and molecular interactions. It's also pivotal in calculating molecular moment of inertia, as this distance partly defines the rotational dynamics of the molecule in question.
Mass of Cesium Atom
In physics, the mass of components like cesium atoms is essential for calculations involving motion. For example, in calculating the moment of inertia for a molecule, the mass and distance from the axis of rotation are vital. By understanding how cesium's mass affects these calculations, we gain insight into the molecule's rotational behavior and dynamics.