Randall D. Knight — Interactions and Potential Energy: Problem 55

Figure 10.23 showed the potential-energy curve for the \(O_2\) molecule. Consider a molecule with the energy \(E_1\) shown in the figure. a. What is the maximum speed of an oxygen atom as it oscillates back and forth? Don't forget that the kinetic energy is the total kinetic energy of the system. The mass of an oxygen atom is 16 u, where \(1\text{ u} = 1\text{ atomic mass unit} = 1.66 \times 10^{-27}\text{ kg}\). b. The atom’s speed varies as it oscillates, but you can make the reasonable assumption that the average speed is half the maximum speed. With that assumption, what is the oscillation frequency of an oxygen atom in a molecule that has energy \(E_1\)? Think carefully about how far each atom travels during one cycle. Give your answer in THz, where \(1\text{ THz} = 1\text{ terahertz} = 10^{12}\text{ Hz}\), and \(1\text{ Hz} = 1\text{ hertz} = 1\text{ cycle/s}\) is the unit of frequency.