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Chapter 9: Problem 1316

A diatomic molecule has how many degrees of freedom (For rigid rotator) (A) 4 (B) 3 (C) 6 (D) 5

Short Answer

Expert verified
A diatomic molecule, as a rigid rotator, has 2 degrees of freedom for rotation around the X and Y axes, which are perpendicular to the internuclear axis. However, if we consider 3 translational degrees of freedom, the total degrees of freedom for a diatomic molecule would be 5 (2 rotational + 3 translational). Therefore, the closest correct answer is (D) 5.

Step by step solution

01

Recall the definition of degrees of freedom

Degrees of freedom are the independent ways a system (in this case, a diatomic molecule) can store energy or change its motion. For the rigid rotator model, we only consider the rotational motion.
02

Consider the rotational axes for the diatomic molecule

A diatomic molecule can rotate about the three axes in space: the X, Y, and Z axes. However, the rotation around the axis passing through the bond (internuclear axis) doesn't contribute to any energy change; this is because it is a rigid molecule, and the bond length does not change.
03

Determine the degrees of freedom

Since we only need to take into account two of the three rotational axes (the ones not passing through the bond), the diatomic molecule, as a rigid rotator, has two degrees of freedom: - Rotation around the X-axis (perpendicular to the internuclear axis) - Rotation around the Y-axis (perpendicular to the internuclear axis)
04

Choose the correct answer

From the given options, we can select the answer that corresponds to 2 degrees of freedom. Unfortunately, there is no option that matches 2 as the correct answer. However, if we consider the question in the more general sense (not specifying only the rigid rotator), the diatomic molecule has 3 translational degrees of freedom and 2 rotational degrees of freedom. In this sense, the answer would be: \(3 + 2 = 5\) So, selecting the option (D) 5 would be the closest correct answer in this case.

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Most popular questions from this chapter

The temperature of an ideal gas is increased from \(27^{\circ} \mathrm{C}\) to \(127^{\circ} \mathrm{C}\), then percentage increase in \(\mathrm{v}_{\mathrm{rms}}\) is (A) \(33 \%\) (B) \(11 \%\) (C) \(15.5 \%\) (D) \(37 \%\)

The root mean square velocity of the molecules in a sample of helium is $(5 / 7)^{\text {th }}$ that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is \(0^{\circ} \mathrm{C}\), then the temperature of the helium sample is about (A) \(273^{\circ} \mathrm{C}\) (B) \(0^{\circ} \mathrm{C}\) (C) \(0^{\circ} \mathrm{K}\) (D) \(100^{\circ} \mathrm{C}\)

The average kinetic energy of hydrogen molecules at \(300 \mathrm{~K}\) is \(E\). At the same temperature the average kinetic energy of oxygen molecules will be (A) [E/(16)] (B) \(E\) (C) \(4 \mathrm{E}\) D) \([E /(4)]\)

The temperature of an ideal gas is increased from \(27^{\circ} \mathrm{C}\) to \(927^{\circ} \mathrm{C}\). The root mean square speed of its molecules becomes (A) Four times (B) One-fourth (C) Half (D) Twice

For a gas \(\left(R / C_{V}\right)=0.67\). This gas is made up of molecules which are (A) Diatomic (B) monoatomic (C) polyatomic (D) mixture of diatomic and polyatomic molecules
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