Quantum mechanics is used to describe the vibrational motion of molecules, but analysis using classical physics gives some useful insight. In a classical model the vibrational motion can be treated as SHM of the atoms connected by a spring. The two atoms in a diatomic molecule vibrate about their center of mass, but in the molecule HIHI, where one atom is much more massive than the other, we can treat the hydrogen atom as oscillating in SHM while the iodine atom remains at rest. Part A
A classical estimate of the vibrational frequency is f = 7.0 x 1015 Hz. The mass of a hydrogen atom differs little from the mass of a proton. If the HI molecule is modeled as two atoms connected by a spring, what is the force constant of the spring? Express your answer to two significant figures and include the appropriate units. k= 320 N
Part B
The vibrational energy of the molecule is measured to be about 5 x 10-20 J. In the classical model, what is the maximum speed of the H atom during its SHM? Express your answer to one significant figure and include the appropriate units. v = 8000
Part C
What is the amplitude of the vibrational motion? Express your answer to one significant figure and include the appropriate units. • Ea ? I HÀ A = 3.4.1018 • • m
Part D
How does your result compare to the equilibrium distance between the two atoms in the HI molecule, which is about 1.6 x 10-10 m? Express your answer using one significant figure. IVO AQ R O 2 ? equilibrium distance = 2.25 • 10-2