Reduced Mass of Reactants A and B Calculator

Reduced Mass Formula:

\[ \mu_{AB} = \frac{m_B \times m_B}{m_A + m_B} \]

Reduced Mass of Reactants A and B: kg

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1. What is Reduced Mass of Reactants A and B?

Definition: The reduced mass is an inertial mass appearing in the two-body problem of Newtonian mechanics.

Purpose: It simplifies the two-body problem to an equivalent one-body problem, making calculations easier in physics and chemistry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \mu_{AB} = \frac{m_B \times m_B}{m_A + m_B} \]

Where:

\( \mu_{AB} \) — Reduced mass of reactants A and B (kg)
\( m_A \) — Mass of reactant A (kg)
\( m_B \) — Mass of reactant B (kg)

Explanation: The formula calculates the equivalent mass that would appear in the equations of motion when considering the relative motion of two bodies.

3. Importance of Reduced Mass Calculation

Details: Reduced mass is crucial in molecular physics, quantum mechanics, and celestial mechanics for simplifying two-body problems.

4. Using the Calculator

Tips: Enter the masses of both reactants in kilograms. Both values must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is reduced mass important in chemistry?
A: It's used in calculating vibrational frequencies of diatomic molecules and in collision theory.

Q2: What's the physical interpretation of reduced mass?
A: It represents the "effective mass" in the relative motion of two bodies, where one body appears stationary.

Q3: How does reduced mass affect molecular vibrations?
A: The vibrational frequency of a diatomic molecule is inversely proportional to the square root of the reduced mass.

Q4: Can reduced mass be greater than the individual masses?
A: No, reduced mass is always less than or equal to the smaller of the two masses.

Q5: How is reduced mass used in astronomy?
A: It's used to calculate orbital periods in binary star systems and planet-satellite systems.