# Smallest amount of vibrational energy

Would I use the equation E = 1/2 h√(ks/m) to work out what the smallest amount of vibrational energy that I can add to a system?

Andrew Mason
Homework Helper
Would I use the equation E = 1/2 h√(ks/m) to work out what the smallest amount of vibrational energy that I can add to a system?
If you are referring to a quantum harmonic oscillator, such as the vibration of a diatomic molecule, the energy levels are:

$$E_n = \hbar\omega(n+\frac{1}{2})$$

where $\omega = \sqrt{k/\mu}$, μ being the reduced mass of the system and k being the spring constant.

So the smallest amount of energy it can have is the zero energy level: $E_0 = \hbar\omega/2$. The smallest amount of energy that can be added would be $\hbar\omega$.

AM

Thanks Andrew :)