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Chapter 3: Problem 8

Degrees of freedom in a water molecule are (a) 1 (b) 2 (c) 3 (d) 4

Short Answer

Expert verified
The total number of degrees of freedom for a water molecule is 9.

Step by step solution

01

Identify molecule type

First identify the type of molecule. Water is a triatomic molecule, meaning it has three atoms.
02

Calculate translational degrees of freedom

All molecules, regardless of the number of constituent particles (atoms), always have 3 degrees of freedom corresponding to motion (translation) along the 3 spatial dimensions: x, y, and z.
03

Calculate rotational degrees of freedom

Molecules in three dimensions also have rotation. For nonlinear molecules such as water, there are 3 degrees of freedom corresponding to rotation around the three perpendicular axes.
04

Calculate vibrational degrees of freedom

The vibrational degrees of freedom for any molecule is given by the formula \(3n-6\) for non-linear molecules, where \(n\) is the number of atoms in the molecule. Substituting \(n=3\) for the water molecule, we get \(3*3-6 = 3\) vibrational degrees of freedom.
05

Calculate total degrees of freedom

Finally, add up all the degrees of freedom: translational (3), rotational (3), and vibrational (3) to find the total degrees of freedom.

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