Question

In the (i) absence of electric field, and in the (ii) presence of electric field, the paths of electrons between successive collisions with the positive ions of the metal, are

• A. (i) Straight line, (ii) straight line
• B. (i) Curved, (ii) straight line
• C. (i) Curved, (ii) curved
• D. (i) Straight line, (ii) Curved in general

Hint:

Think of the electron's motion in the presence of an electric field as analogous to a projectile's motion in a uniform gravitational field. Both experience a constant force, leading to a parabolic (curved) trajectory between "collisions" (or from launch to landing).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question describes the motion of free electrons within a metallic conductor under two different conditions: with no external electric field and with an external electric field. We need to determine the nature of the electron's path between two consecutive collisions with the lattice ions.

Step 2: Detailed Explanation:
(i) In the absence of an electric field:
The free electrons in a metal are in constant random motion due to thermal energy. Between two successive collisions with the positive ions of the metal lattice, there is no net force acting on an electron (ignoring gravitational forces, which are negligible). According to Newton's first law, an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Therefore, the electron travels in a straight line at a constant velocity between collisions.
(ii) In the presence of an electric field:
When an external electric field (\(\vec{E}\)) is applied, each electron experiences a constant electrostatic force \(\vec{F} = -e\vec{E}\). This constant force causes the electron to have a constant acceleration (\(\vec{a} = \vec{F}/m_e = -e\vec{E}/m_e\)) in the direction opposite to the field. An object moving with an initial velocity and subject to a constant acceleration follows a parabolic path. Thus, the path of the electron between successive collisions becomes curved. The overall motion is a combination of random thermal velocity and a directed drift caused by the field.

Step 3: Final Answer:
In the absence of an electric field, the path is a straight line. In the presence of an electric field, the path is curved due to the constant electrostatic force.