Reduced Mass Calculator

What Is Reduced Mass?

Reduced mass simplifies two-body problems into an equivalent one-body system. It appears in molecular vibrations, binary orbits, collision theory, and quantum mechanics. The reduced mass is always less than or equal to the lighter of the two masses.

Reduced Mass Formula

For two masses $m_1$ and $m_2$:

$$\mu = \frac{m_1 m_2}{m_1 + m_2}$$

When one mass is much larger than the other, the reduced mass approaches the smaller mass. For a hydrogen atom, the reduced mass is slightly less than the electron mass because the proton also moves.

Where Reduced Mass Appears

The vibrational frequency of a diatomic molecule depends on reduced mass. In celestial mechanics, two orbiting bodies follow paths as if a single body of mass mu orbited their common center of mass. Collision cross-sections also use reduced mass.

Frequently Asked Questions

What is the reduced mass of two equal masses?

When m1 equals m2, the reduced mass is half of either mass. For two 10 kg objects, mu equals 5 kg.

Why is reduced mass always less than the lighter mass?

The formula mu = m1*m2/(m1+m2) is always smaller than min(m1, m2). Both masses contribute to the denominator, pulling the result below the lighter value.

How is reduced mass used in molecular vibrations?

The vibrational frequency of a diatomic bond depends on the force constant and reduced mass. Lighter atoms vibrate faster because mu appears in the denominator of the frequency formula.

What happens when one mass is very large?

If m1 is much larger than m2, the reduced mass approaches m2. For a planet orbiting the Sun, the reduced mass is essentially the planet's mass.

What units should I use?

Use consistent mass units, typically kilograms. The reduced mass has the same units as the input masses.

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What Is Reduced Mass?

Reduced Mass Formula

Where Reduced Mass Appears

Frequently Asked Questions

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