Question

Repeat problem 9 for an oxygen molecule, $\mathrm{O}_2$, given that the mass of an oxygen atom is $2.67 \times 10^{-26} \mathrm{~kg}$ and the interatomic spacing is $1.21 \times 10^{-10} \mathrm{~m}$.

   Repeat problem 9 for an oxygen molecule, $\mathrm{O}_2$, given that the mass of an oxygen atom is $2.67 \times 10^{-26} \mathrm{~kg}$ and the interatomic spacing is $1.21 \times 10^{-10} \mathrm{~m}$.
An Introduction to Thermodynamics and Statistical Mechanics
An Introduction to Thermodynamics and Statistical Mechanics
Keith Stowe 2nd Edition
Chapter 4, Problem 10 ↓
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Repeat problem 9 for an oxygen molecule, $\mathrm{O}_2$, given that the mass of an oxygen atom is $2.67 \times 10^{-26} \mathrm{~kg}$ and the interatomic spacing is $1.21 \times 10^{-10} \mathrm{~m}$.
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An oxygen molecule consists of two oxygen atoms whose total mass is $5.3 \times 10^{-26} \mathrm{~kg}$ and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9 \times 10^{-46} \mathrm{~kg} \cdot \mathrm{m}^{2}$. From these data, estimate the effective distance between the atoms.

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(II) An oxygen molecule consists of two oxygen atoms whose total mass is $5.3 \times 10^{-26} \mathrm{kg}$ and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9 \times 10^{-46} \mathrm{kg} \cdot \mathrm{m}^{2} .$ From these data, estimate the effective distance between the atoms.

Physics for Scientists and Engineers with Modern Physics


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Transcript

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00:01 Here i'll be looking at the concept of moment of inertia, which is a rotational analog of mass.
00:18 So in other words, if we look at the rotational analog of f equals ma, which is torque equals i times alpha, i is moment of inertia, the larger moment of inertia is the moment of inertia is the harder the object is.
00:40 To rotate in a similar fashion to the larger mass.
00:49 An object has the harder it is to accelerate along a straight line.
00:55 Here we're going to specifically talk about the moment of inertia of a point mass is equal to the mass itself times d squared, where d is the distance to the axis of rotation.
01:18 So this is how it's a little bit different than in a linear sense.
01:24 The distance or radius always matters when it comes to rotations.
01:30 And here as an example, we're going to take a look at an oxygen molecule, which consists of two oxygens with a bond in between them.
01:46 Each of the oxygen nuclei have a mass.
01:51 Here we'll say 5 .3.
01:53 Times 10 to the minus 26 kilograms, which is about 18 times 16 to 18 times the mass of a nucleus, a nucleon, a neutron or proton.
02:10 Let's see.
02:13 And that looks to be oxygen 16, we believe.
02:17 And there's some axis of rotation that is occurring right in between the two...
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