Frequency from Temperature Calculation

This calculator computes the vibrational frequency of molecules based on temperature using the equipartition theorem. It can be used to understand how temperature affects molecular vibrations in materials.

Input Parameters

Calculation Results

Calculation Formula

Frequency (ν) = √(k·T)/(2π·m)

Where:
ν = Vibrational frequency (Hz)
k = Boltzmann constant (1.380649 × 10⁻²³ J/K)
T = Temperature (K)
m = Mass (kg)
π = 3.14159265359

Results

Boltzmann Constant (k): 1.380649 × 10⁻²³ J/K
Planck Constant (h): 6.62607015 × 10⁻³⁴ J·s
Classical Frequency: --
Quantum Harmonic Frequency (ω = √(k/m)): --
Energy at Temperature (E = hω): --

Frequency from Temperature Calculation Calculator Usage Guide

Learn how to use the calculator for understanding molecular vibrations and thermal energy distribution

How to Use This Calculator

  1. Enter the molecular mass in kilograms. For diatomic molecules, this is half the total molecular mass.
  2. Input the spring constant (force constant) of the molecule's bonds in Newtons per meter.
  3. Specify the temperature in Kelvin.
  4. Choose the molecule type (diatomic, monatomic, or custom).
  5. 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.