define mobility of electron in a conductor. How does electron mobility change when (i) temperature of conductor is decreased (ii) Applied potential difference is doubled at constant temperature?

Electron mobility in a conductor refers to how easily electrons can move through the material when an electric field is applied. It is a crucial property that determines the conductivity of the material. The mobility of electrons is influenced by various factors, including temperature and the applied potential difference. Let's delve into how these factors affect electron mobility.

Understanding Electron Mobility

Electron mobility, denoted by the symbol μ, is defined as the velocity of the electrons per unit electric field. Mathematically, it can be expressed as:

μ = v / E

where v is the drift velocity of the electrons and E is the electric field strength. Higher mobility means that electrons can move more freely, contributing to better conductivity.

Effect of Temperature on Electron Mobility

When the temperature of a conductor is decreased, the mobility of electrons generally increases. This can be explained through the following points:

• Reduced Thermal Vibrations: At lower temperatures, the lattice structure of the conductor experiences less thermal agitation. This means that the atoms in the lattice vibrate less, creating fewer obstacles for the electrons to navigate through.
• Increased Mean Free Path: As the temperature drops, the mean free path—the average distance an electron travels between collisions—increases. This allows electrons to move more freely without scattering off impurities or lattice imperfections.

As a result, the overall conductivity of the material improves as the temperature decreases, leading to higher electron mobility.

Impact of Doubling the Applied Potential Difference

When the applied potential difference across a conductor is doubled while keeping the temperature constant, the effect on electron mobility is a bit different:

• Increased Drift Velocity: Doubling the potential difference increases the electric field strength, which in turn increases the drift velocity of the electrons. However, this does not necessarily mean that the mobility itself increases.
• Scattering Effects: At higher electric fields, electrons may experience more frequent collisions with lattice ions, impurities, or other electrons. This can lead to a phenomenon known as "saturation" where the mobility becomes constant despite increases in the electric field.

In essence, while the drift velocity increases with a higher applied potential difference, the mobility may not change significantly, and in some cases, it could even decrease due to increased scattering effects.

Summary

To summarize, electron mobility in a conductor is a key factor in determining its conductivity. Lowering the temperature typically enhances electron mobility by reducing thermal vibrations and increasing the mean free path. Conversely, doubling the applied potential difference at constant temperature increases the drift velocity but may not significantly affect mobility due to increased scattering. Understanding these concepts is essential for grasping the behavior of conductors in various electrical applications.