A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance

Q: Why does copper's resistance decrease when cooled?

In metals, resistance is primarily caused by electrons colliding with vibrating atoms in the lattice. Cooling reduces these thermal vibrations, allowing electrons to flow with fewer collisions.

Q: Why does germanium behave oppositely to copper?

Germanium is a semiconductor. Its ability to conduct relies on thermal energy breaking covalent bonds to create free electrons and holes. Cooling removes this energy, drastically reducing the number of charge carriers.

Q: Does the resistance of copper ever reach zero if we keep cooling it?

For normal metals like copper, no. It plateaus at a small 'residual resistance' due to impurities and structural defects. Only special materials called superconductors drop to exactly zero resistance.

Q: What happens to germanium at absolute zero (0 K)?

At absolute zero, there is no thermal energy to break any bonds. Germanium becomes a perfect insulator with theoretically infinite resistance.

Q: Is this temperature dependence linear for both materials?

For metals like copper, it is approximately linear over a wide range of temperatures. However, for semiconductors like germanium, the carrier concentration (and thus resistance) changes exponentially with temperature.

Question

A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance of

Options:

(A) each of them increases

(B) each of them decreases

(C) copper decreases and germanium increases

(D) copper increases and germanium decreases

Sigma Percentile · Accepted Answer

### The Tale of Two Materials

Imagine you have two distinct pieces of material sitting on your desk at room temperature: a shiny piece of copper and a dark, crystalline piece of germanium. You decide to plunge both of them into a bath of liquid nitrogen, rapidly cooling them down to a freezing $77 	ext{ K}$. What happens to their electrical resistance? To answer this, we must dive into the microscopic world of atoms and electrons.

### The Metal's Perspective: Copper

Copper is a classic metal, a brilliant conductor of electricity. In a metal, the outer electrons of the atoms are free to roam, forming a "sea of electrons." However, the atoms themselves are arranged in a lattice, and at room temperature, they vibrate vigorously due to thermal energy. These vibrations act like obstacles, scattering the flowing electrons and creating electrical resistance.

When we cool the copper down to $77 	ext{ K}$, we are essentially draining thermal energy from the system. The lattice vibrations calm down significantly. With fewer obstacles in their path, the electrons can flow much more smoothly. Therefore, **for a conductor like copper, as temperature decreases, its resistance decreases.**

### The Semiconductor's Perspective: Germanium

Germanium, on the other hand, is a semiconductor. Its behavior is governed by a completely different set of rules. At absolute zero, a semiconductor is a perfect insulator because all its electrons are tightly bound in covalent bonds. At room temperature, thermal energy is sufficient to break some of these bonds, exciting electrons into the conduction band and leaving behind "holes" in the valence band. These thermally generated electrons and holes are what allow germanium to conduct electricity.

When we cool the germanium down to $77 	ext{ K}$, we are taking away the very thermal energy it relies on to generate charge carriers. The electrons fall back into their bonds, and the number of available charge carriers plummets exponentially. With fewer carriers available to transport charge, the material becomes much less conductive. Therefore, **for a semiconductor like germanium, as temperature decreases, its resistance increases.**

### The Final Verdict

By understanding the fundamental differences in how metals and semiconductors conduct electricity, the answer becomes crystal clear. The cooling process calms the lattice vibrations in copper, making it a better conductor (resistance decreases). Simultaneously, it freezes the charge carriers in germanium, making it a worse conductor (resistance increases).

Animated Solution for Physics - Semiconductors: A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance of

Select Answer:

Visualized Solution

\text{Material Identification}

\text{Conductors: } R \text{ vs } T

\text{Semiconductors: } R \text{ vs } T

\text{Conclusion}

\text{Food for Thought}

The Sigma Insight: Energy Bands in Solids and Semiconductors

The Tale of Two Materials

The Metal's Perspective

The Semiconductor's Perspective

The Final Verdict

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