Reduced Mass of Reactants using Collision Frequency Calculator

Reduced Mass Formula:

\[ \mu_{AB} = \left(\frac{n_A \times n_B \times \sigma_{AB}}{Z}\right)^2 \times \frac{8 \times k_B \times T}{\pi} \]

Number Density for A Molecules:

mol/m³

Number Density for B Molecules:

mol/m³

Collisional Cross Section:

m²

Collision Frequency:

m³/s

Temperature:

Reduced Mass (kg):

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1. What is Reduced Mass of Reactants?

Definition: Reduced mass is an inertial mass appearing in the two-body problem of Newtonian mechanics that simplifies the analysis of particle collisions.

Purpose: It helps in analyzing molecular collisions and reaction kinetics by providing an equivalent mass for the two-particle system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \mu_{AB} = \left(\frac{n_A \times n_B \times \sigma_{AB}}{Z}\right)^2 \times \frac{8 \times k_B \times T}{\pi} \]

Where:

\( \mu_{AB} \) — Reduced mass of reactants A and B (kg)
\( n_A \) — Number density for A molecules (mol/m³)
\( n_B \) — Number density for B molecules (mol/m³)
\( \sigma_{AB} \) — Collisional cross section (m²)
\( Z \) — Collision frequency (m³/s)
\( k_B \) — Boltzmann constant (1.38×10⁻²³ J/K)
\( T \) — Temperature (K)
\( \pi \) — Pi constant (3.1416)

3. Importance of Reduced Mass Calculation

Details: Reduced mass is crucial for understanding collision dynamics, reaction rates, and energy transfer in molecular systems.

4. Using the Calculator

Tips: Enter all required parameters (number densities, cross section, collision frequency, and temperature). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of reduced mass?
A: It represents the "effective" mass of a system of two particles when treated as a single object in their center-of-mass frame.

Q2: How does temperature affect reduced mass?
A: Higher temperatures increase the kinetic energy term in the calculation, potentially leading to higher reduced mass values.

Q3: What are typical values for collisional cross section?
A: Typical molecular collision cross sections range from 10⁻¹⁹ to 10⁻¹⁸ m², depending on molecular size.

Q4: Why is Boltzmann constant used here?
A: It relates the average kinetic energy of particles to the temperature, which is fundamental to collision dynamics.

Q5: Can this be used for identical particles?
A: Yes, when A and B are the same, the reduced mass simplifies to half the mass of one particle.