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Chapter 11: Problem 34

A molecule has a rotational inertia of \(14,000 \mathrm{u} \cdot \mathrm{pm}^{2}\) and is spinning at an angular speed of \(4.30 \times 10^{12} \mathrm{rad} / \mathrm{s}\). (a) Express the rotational inertia in \(\mathrm{kg} \cdot \mathrm{m}^{2} .(b)\) Calculate the rotational kinetic energy in \(\mathrm{eV}\).

Short Answer

Expert verified
The rotational inertia of the molecule in \(kg \cdot m^2\) is calculated in step 1. Using this value and the provided angular speed, the kinetic energy of the molecule (in Joules) is determined in step 2. The kinetic energy is then converted to electron volts in step 3. This series of conversions and calculations lead to the final answer.

Step by step solution

01

Convert unit of rotational inertia

To convert the unit of rotational inertia from \(14,000 u \cdot pm^2\) to \(kg \cdot m^2\), use these conversion factors: \(1 u = 1.660539040 \times 10^{-27} kg\) and \(1 pm = 10^{-12} m\). Therefore, by multiplying by these conversion factors, get the rotational inertia in the required unit.
02

Calculate rotational kinetic energy

The rotational kinetic energy (\(Ek\)) can be calculated using the formula \(Ek = \frac{1}{2} I \omega^2\), where \(I\) is the rotational inertia and \(\omega\) is the angular speed. Substituting the given values \(\omega = 4.30 \times 10^{12} rad/s\) and the converted \(I\) from step 1 into the formula, find \(Ek\) in Joules, which is the SI unit of energy.
03

Convert energy to electron volts

Given \(1 eV = 1.602 \times 10^{-19} J\), convert the obtained rotational kinetic energy to electron volts by dividing the energy in Joules by the conversion factor.

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Most popular questions from this chapter

A swimmer moves through the water at a speed of \(0.22 \mathrm{~m} / \mathrm{s}\). The drag force opposing this motion is \(110 \mathrm{~N}\). How much power is developed by the swimmer?

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