Question

In Classical Physics, the typical simple harmonic oscillator is a mass attached to a spring. The natural frequency of vibration (radians per second) for a simple harmonic oscillator is given by ω=√k/m and it can vibrate with ANY possible energy whatsoever. Consider a mass of 135 grams attached to a spring with a spring constant of k = 1 N/m. What is the Natural Frequency (in rad/s) of vibration for this oscillator?

In Quantum Mechanics, the energy levels of a simple harmonic oscillator are QUANTIZED and are given by En=(n+1/2)ℏ, where n = 1, 2, 3, 4, ….. Hence, the spacing between adjacent energy levels for a simple harmonic oscillator must be ΔE=ℏω. What is the spacing between the energy levels (in eV) for the oscillator in this problem? (Does this explain why we do NOT notice energy quantization for Macroscopic (large-sized) objects?)

Now consider a Microscopic (atomic-sized) object, such as a diatomic hydrogen molecule (H₂). In such a system, the bond between the hydrogen atoms can be modeled as a spring with a spring constant of k = 510 N/m, and the atoms can vibrate back and forth as a simple harmonic oscillator with an effective mass of m = 8.37 x 10^-28 kg. What is the Natural Frequency (in rad/s) of vibration for this molecule?

What is the spacing between the energy levels (in eV) for the oscillator (diatomic hydrogen molecule) in this problem? (Does this explain why energy quantization is VERY noticeable for Microscopic (atomic-sized) objects?)

Answer 1