Reduced Mass
Definition and meaning of Reduced Mass in chemistry.
Reduced mass is the effective mass of two particles that interact with each other, calculated as μ = m₁m₂/(m₁ + m₂) where m₁ and m₂ are the individual masses. It simplifies two-body problems into an equivalent one-body problem.
In more detail
In molecules with two atoms (or any two-body system), the reduced mass replaces the need to track both particles separately. This is especially useful in quantum mechanics and spectroscopy, where it determines vibrational frequencies and rotational properties. The reduced mass is always less than both individual masses. For a symmetric diatomic molecule like H2, the reduced mass equals exactly half the mass of one hydrogen atom.
Key facts
| Symbol | μ (mu) |
|---|---|
| Formula | μ = m₁m₂/(m₁ + m₂) |
| Field | Physical Chemistry |
| Units | Same as individual masses (u, g, kg) |
In a carbon monoxide molecule (CO), the reduced mass μ is calculated from the atomic mass of carbon (approximately 12 u) and oxygen (approximately 16 u): μ = (12 × 16)/(12 + 16) = 6.86 u. This value is used in equations to calculate the CO vibrational frequency.
Frequently asked questions
Why use reduced mass instead of individual atomic masses?
Reduced mass describes the relative motion of two particles around their center of mass, which is essential for calculating molecular vibrations and rotations in quantum mechanics.
How does reduced mass affect molecular vibrational frequency?
Vibrational frequency is proportional to the square root of (bond strength/reduced mass). Lighter reduced mass leads to higher frequency, so C-H bonds vibrate faster than C-Cl bonds.