How is a relaxation time measured in physics and chemistry?

In physics and chemistry, a relaxation time ($\tau$) is measured by observing how a system returns to equilibrium after being subjected to a small disturbance. Because these processes are often extremely fast, researchers use specialized detection techniques to monitor the system's response over time.12

Measurement Techniques

The specific method depends on the nature of the relaxation effect:

• Spectroscopy and Detection: Changes in a system can be monitored using absorption or emission spectroscopy, fluorometry, polarimetry, or by measuring changes in conductance.1
• Flash Photolysis: To study rapid photochemical reactions, researchers use sequences of light pulses. An intense pulse creates an excited state, and a subsequent weaker pulse probes the transient absorption to track the system's evolution. Modern experiments utilize lasers to achieve time resolutions as short as 10 femtoseconds.2
• Nuclear Magnetic Resonance (NMR): In NMR spectrometry, relaxation times are determined by measuring the time it takes for excited nuclei to dissipate excess energy and return to their low-energy orientation within a magnetic field.3
• Sound Propagation: Historically, measuring the absorption of sound waves through gases has been used to evaluate energy transfer between molecular degrees of freedom.4

Mathematically, the rate of disappearance of a small displacement from equilibrium is typically proportional to the magnitude of that displacement, allowing the process to be described by a first-order differential equation. The relaxation time is defined as the reciprocal of the constant of proportionality in this relationship.1