Question

Assertion and reason are given in following questions each question has four options one of them is correct select it. (a) Both assertion and reason are true and the reason is correct reclamation of the assertion. (b) Both assertion and reason are true, but reason is not correct explanation of the assertion. (c) Assertion is true, but the reason is false. (d) Both, assertion and reason are false. Assertion: the drift velocity of electrons in a metallic wire will decrease, if the temperature of the wire is increased Reason: On increasing temperature, conductivity of metallic wire decreases. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) d

Short answer

The correct option is (A) a: Both assertion and reason are true, and the reason is the correct reclamation of the assertion. The drift velocity of electrons decreases when the temperature of the metallic wire increases because the conductivity of the wire decreases due to increased collisions between free electrons and lattice atoms.

Step-by-step solution

1. Understand drift velocity and conductivity

Drift velocity is the average velocity of charge carriers, such as electrons, in a conducting material when an electric field is applied. Conductivity (σ) is a measure of a material's ability to conduct an electric current. In a metal, the conductivity mainly depends on the number of free electrons available and their mobility.

2. Analyze the effect of temperature on drift velocity

When the temperature of a metal wire is increased, the thermal vibrations of the atoms in the lattice increase. This increased vibration results in more frequent collisions between the free electrons and the lattice, which leads to a decrease in the average drift velocity of electrons.

3. Analyze the effect of temperature on conductivity

Conductivity in metals is inversely proportional to the resistivity (ρ), which increases with temperature due to the increased collision rate between electrons and lattice atoms. Therefore, when the temperature of a metallic wire increases, its conductivity decreases, as mentioned in the given reason.

4. Determine the relationship between assertion and reason

The assertion states that drift velocity decreases when the temperature increases, and the reason states that conductivity decreases when the temperature increases. Both statements are true, and the decrease in conductivity is linked to the decrease in drift velocity. Therefore, the reason is the correct explanation of the assertion.

5. Select the correct option

Since both the assertion and reason are true, and the reason is the correct explanation for the assertion, the correct choice is (A) a: Both assertion and reason are true and the reason is the correct reclamation of the assertion.

Key concepts

Electron Mobility

Electron mobility refers to how quickly electrons can move through a conductor when an electric field is applied. It is a crucial factor in determining the drift velocity, which is the average velocity of electrons under the influence of the electric field. The mobility itself depends on two main things:

• The number of free electrons available in the material.
• The environment through which these electrons move, meaning how often they collide with atoms in the lattice structure.

Higher electron mobility results in higher drift velocities. When a material has high electron mobility, it means that electrons can move through it more freely, encountering fewer obstacles in the form of collisions with other atoms. This makes the material a better conductor of electricity.

Conductivity in Metals

Conductivity is the ability of a material to allow the flow of electric current. In metals, this property is primarily determined by the number of free electrons available to move freely. The conductivity (\(σ\)) of a material is affected by:

• The density of free electrons.
• The mobility of these electrons within the material.

Metals are known for their excellent conductivity due to a high number of free electrons that can move easily, making them ideal conductors. The relationship between conductivity and resistivity (\(ρ\)) is given by the equation:\[σ = \frac{1}{ρ}\]Where high conductivity implies low resistivity and vice versa. This interplay between electron density and mobility dictates how efficiently a metal conducts electricity.

Temperature Effect on Conductors

Temperature has a significant impact on the conductive properties of metals. As the temperature increases, several changes occur:

• The lattice atoms vibrate more vigorously, leading to more frequent collisions with the free electrons.
• These collisions hinder electron movement, thereby reducing the drift velocity.
• The increased collisions cause resistivity to rise, which decreases the overall conductivity of the metal.

The general rule is that an increase in temperature results in higher resistivity and reduced conductivity. This is because the thermal energy provided at higher temperatures increases the vibrations of atoms in the metal lattice, leading to more collisions and scattering of electrons. This relationship is crucial in understanding why cooling a metal increases its conductivity, making it possible for electrons to glide more smoothly with fewer interruptions.