How to Use This Calculator
- Enter the molecular mass in kilograms. For diatomic molecules, this is half the total molecular mass.
- Input the spring constant (force constant) of the molecule's bonds in Newtons per meter.
- Specify the temperature in Kelvin.
- Choose the molecule type (diatomic, monatomic, or custom).
- Click the "Calculate" button to compute the vibrational frequency and related properties.
Understanding the Results
This calculator shows both classical and quantum mechanical approaches to molecular vibrations:
- Classical Frequency: Represents the expected vibration frequency based on classical mechanics, assuming the bond behaves like a spring.
- Quantum Harmonic Frequency: Represents the angular frequency of the quantum harmonic oscillator model, which is a better approximation for molecular vibrations.
- Energy at Temperature: Shows the thermal energy of the vibration at the given temperature using the Planck constant.
Applications
This calculator can be used in:
- Chemistry education to understand molecular dynamics
- Material science for analyzing thermal properties of materials
- Physics for studying thermal energy distribution in gases and solids
- Understanding spectroscopic phenomena like infrared absorption
Example Calculation
For a diatomic molecule like carbon monoxide (CO) with a mass of 28.01 g/mol (0.02801 kg/mol) and a spring constant of 1860 N/m at 300 K:
Classical frequency would be approximately 1.42 × 10¹³ Hz, which falls in the infrared region of the electromagnetic spectrum.