1. What is Temperature given Vibrational Energy of Linear Molecule?

Definition: This calculator determines the temperature of a linear molecule based on its vibrational energy and atomicity.

Purpose: It helps in understanding the relationship between molecular vibrations and temperature in thermodynamics and quantum chemistry.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T \) — Temperature (Kelvin)
• \( E_{vf} \) — Vibrational Energy (Joules)
• \( N \) — Atomicity (number of atoms in the molecule)
• \( [BoltZ] \) — Boltzmann constant (1.38064852 × 10⁻²³ J/K)

Explanation: The vibrational energy is divided by the degrees of freedom (3N-5 for linear molecules) multiplied by Boltzmann's constant to obtain temperature.

3. Importance of This Calculation

Details: Understanding this relationship is crucial in spectroscopy, thermodynamics, and molecular physics to interpret energy states and temperature effects.

4. Using the Calculator

Tips: Enter the vibrational energy in Joules and the atomicity (minimum 2 for a molecule). The atomicity must be ≥ 2.

5. Frequently Asked Questions (FAQ)

Q1: Why is the formula different for linear molecules?
A: Linear molecules have 3N-5 vibrational degrees of freedom (rather than 3N-6 for nonlinear molecules) due to their symmetry.

Q2: What is vibrational energy?
A: Vibrational energy is the energy associated with the vibrational motions of atoms in a molecule.

Q3: What's the range of typical vibrational energies?
A: Molecular vibrational energies typically range from 10⁻²² to 10⁻¹⁹ Joules, depending on the molecule.

Q4: Can this be used for nonlinear molecules?
A: No, for nonlinear molecules you would use 3N-6 instead of 3N-5 in the denominator.

Q5: Why is Boltzmann's constant important here?
A: Boltzmann's constant relates energy at the molecular level to macroscopic temperature.