# Zero Point Energy

## Zero Point Energy

Zero point energy is the energy which a molecule must have even at absolute zero temperature. Therefore, even at absolute temperature when rotational and translational motions stop, vibrational motion still persists.For a diatomic molecule, the two atoms of which are supposed to vibrate harminically with respect to each other. The zero point energy (E

_{o}) per mole is given by-

where, N = Avogadro number

h = Plank's constant

c = Velocity of light

ω

_{e}= Equilibrium vibrational frequency per centimeter.

If vibration of the atom is simple harmonic in nature then the value of ω

_{e}is related to the restoring force (f) acting between atoms by the equation-

where, μ = reduced mass.

### Restoring Force

The force which is always directed towards the mean position during an oscillatory motion is called restoring force. That means restoring force is a force acting against the displacement in order to bring back the system in equilibrium.The restoring force is a function that depends on the position of an object or system. This type of force is responsible for generating oscillations and is necessary for an object to be in moving in simple harmonic motion.

Restoring Force(F) = -k x

where,

k = proportionality constant called spring constant

d = distance.