
(a)
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond.
(a)

Answer to Problem 13P
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond is
Explanation of Solution
A hydrogen molecule makes a transition from ground level to
Write the formula for energy levels.
Here,
Refer equation (I) and find energy of
Here,
Refer equation (I) and find energy of
Here,
Refer equation (I) and find energy of
Here,
Write the formula for the energy difference between
Here,
Write the formula for the energy difference between
Here,
Subtract equation (III) from (II).
Re-write the above equation.
Re-write the above equation to obtain
Conclusion:
Substitute
The moment of inertia of the hydrogen molecule about an axis through its center of mass and perpendicular to H-H bond is
(b)
The vibrational frequency of the hydrogen molecule.
(b)

Answer to Problem 13P
The vibrational frequency of the hydrogen molecule is
Explanation of Solution
Refer section (a) and write the formula for the energy difference between
Here,
Re-write the above equation to get an expression for
Write the formula for
Here,
Conclusion:
Substitute
Substitute
The vibrational frequency of the hydrogen molecule is
(c)
The equilibrium separation distance for the molecule.
(c)

Answer to Problem 13P
The equilibrium separation distance for the molecule is
Explanation of Solution
Write the formula for the moment of inertia of the molecule.
Here,
Reduced mass of hydrogen molecule is half of the mass of it.
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The equilibrium separation distance for the molecule is
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Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics
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