In a conductor(A) there are many free electrons and heavy positive io…

The correct answer is Option (3) → (A), (B) and (D) only

These statements describe the free-electron picture of a metal used to explain drift and resistance.

(A) there are many free electrons and heavy positive ions. — Correct. The valence electrons are free to move through a lattice of fixed, heavy positive ions.

(B) ions keep on vibrating about their mean positions. — Correct. The ions are bound to their lattice sites and have thermal vibrations about them.

(C) average amplitude of vibrating ions does not depend on the temperature. — Incorrect. The amplitude increases with temperature; this increases collisions, which is why the resistance of a metal rises when it is heated.

(D) the direction of a free electron after colliding with an ion is completely random. — Correct. Because the velocity after a collision is random, the average thermal velocity is zero, and only the small drift due to an applied field gives a current.

NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “As remarked before, an electron will suffer collisions with the heavy fixed ions, but after collision, it will emerge with the same speed but in random directions.”

Drift of Electrons and the Origin of Resistivity – “… At a temperature \( T \), the thermal speed* of a copper atom of mass \( M \) is obtained from \( [\langle (1/2) Mv^{2} \rangle = (3/2) k_B T] \) and is thus typically of the order of \( \sqrt{k_B T/M} \), where \( k_B \) is the Boltzmann constant. For copper at 300 K, this is about 2 × 10² m/s. This figure indicates the random vibrational speeds of copper atoms in a conductor.”