Relaxation Time
The average time interval between two successive collisions of an electron with the positive ions in the conductor.
What is Relaxation Time?
The average time interval between two successive collisions of a free electron with the positive ions (lattice) in a conductor.
Key formula / rule: Drift Velocity
Key points
- Define relaxation time.
- Explain its significance in electron motion within conductors.
- Relate relaxation time to drift velocity and conductivity.
- Understand the factors affecting relaxation time.
Common exam trap
Confusing relaxation time with the time period of electron oscillation.
Definitions
- Term
Relaxation Time (τ)
- Meaning
The average time interval between two successive collisions of a free electron with the positive ions (lattice) in a conductor.
- Term
Mobility (μ)
- Meaning
The measure of how easily a charge carrier can move through a conductor under the influence of an electric field. It is defined as the drift velocity per unit electric field.
Learning objectives
Define relaxation time.
Explain its significance in electron motion within conductors.
Relate relaxation time to drift velocity and conductivity.
Understand the factors affecting relaxation time.
Formulae
- Name
Drift Velocity
- Note
Where vd is drift velocity, e is the charge of an electron, E is the applied electric field, τ is the relaxation time, and m is the mass of an electron.
- Expression
vd = (eEτ)/m
- Name
Mobility
- Note
Mobility (μ) is the magnitude of drift velocity per unit electric field. It's directly proportional to relaxation time.
- Expression
μ = vd / E = (eτ) / m
- Name
Electrical Conductivity
- Note
Where σ is conductivity, n is the number density of free electrons, e is the charge of an electron, τ is the relaxation time, and m is the mass of an electron.
- Expression
σ = (ne²τ) / m
Prerequisites
Kinetic Theory of Gases
Electric Current
Drift Velocity
Mobility
Common mistakes
Confusing relaxation time with the time period of electron oscillation.
Assuming relaxation time is constant for all electrons.
Not considering the effect of temperature on relaxation time.
Keywords
Relaxation Time
Electron Collision
Drift Velocity
Mobility
Conductivity
Electric Field
Lattice Vibrations
Conductor
Practice preview
The mobility (μ) of charge carriers in a conductor is defined as the magnitude of drift velocity per unit electric field. How is relaxation time (τ) related to mobility (μ)?…
medium
In a metallic conductor, as the temperature increases, the relaxation time of electrons generally:…
medium
What is the average time interval between two successive collisions of an electron with the positive ions in a conductor called?…
easy