# Units of Force Constant

## Homework Statement

A molecule is a harmonic oscillator, and has a fundamental frequency of 1000 cm−1 and a reduced mass of 10.0 amu. From this, determine the magnitude of the force constant, and express it in units of aJ ˚A−2 (atto joules per angstrom).

ω=√(k/mr)

## The Attempt at a Solution

My question is about the requested units. Force constants of harmonic oscillators are given as force*distance, no? So the request for the units in energy/distance2 doesn't make sense. Further, using the relevant equation given I end up with amu/cm2, or mass/distance2. I suppose wavenumbers can be counted as energy as well. Even then, you'd end up with J^2*amu or J*amu/cm. The problem, then, is the remaining mass. I'm fairly certain I'm misunderstanding something in this, however. Any help would be appreciated.

Edit: Apologies for having to move my thread. This is this first part of a multistep quantum mechanical problem. I guess this part is technically more introductory.

Last edited:

vela
Staff Emeritus
Homework Helper
No. The force constant is ##k## as in ##F=-kx## in Hooke's law.

No. The force constant is ##k## as in ##F=-kx## in Hooke's law.
Sorry, I meant force/distance. My question still stands.

vela
Staff Emeritus
Homework Helper
Energy has units of force times distance, so…

Energy has units of force times distance, so…

I know but the problem is the units of this problem itself. I need the units to be in energy/distance^2 which is proper but the output of the equation includes mass and energy (amu and wavenumbers^2) which, from what I can tell, can't be converted to any form of a force constant, which is why I'm sure I'm doing something wrong.

Pulling apart the given equation, it tells us that k = ω2mr. Omega is in wave numbers which is an energy unit, and mr is a reduced mass in units of amu. So E2* mass (from the equation) should be equal to energy/distance2 (from the requested unit in the problem). This is clearly not true, unless Energy is equal to inverse distance2 times mass.

vela
Staff Emeritus
Homework Helper