Question

Copper and silicon is cooled from 300 K to 60 K, the specific resistance

• A. decrease in copper but increase in silicon
• B. increase in copper but decrease in silicon
• C. increase in both
• D. decrease in both.

Answer 1

The Correct Option is A

To determine the behavior of the specific resistance (or resistivity) of copper and silicon as they are cooled from 300 K to 60 K, we need to understand the different temperature-dependent behaviors of conductors and semiconductors.

1. Copper (Conductor):
   • Copper is a metallic conductor. The resistivity of conductors decreases with a decrease in temperature. This is because the thermal vibrations of the lattice, which impede the flow of electrons, diminish at lower temperatures.
   • The relationship between resistivity and temperature for conductors is approximately linear and can be given by the formula: \(\rho(T) = \rho_0 [1 + \alpha(T - T_0)]\) where \(\rho_0\) is the resistivity at a reference temperature \(T_0\), \(\alpha\) is the temperature coefficient of resistance, and \(T\) is the temperature.
   • As the temperature decreases from 300 K to 60 K, the specific resistance of copper decreases.
2. Silicon (Semiconductor):
   • Silicon is a semiconductor. In semiconductors, the resistivity increases as the temperature decreases. This is mainly because fewer charge carriers (electrons and holes) are available at lower temperatures.
   • At higher temperatures, more electrons gain enough energy to move from the valence band to the conduction band, decreasing resistivity. Conversely, at lower temperatures, this energy is insufficient, leading to an increase in resistivity.

Based on these principles, the correct answer is: decrease in copper but increase in silicon.

Hence, when copper and silicon are cooled from 300 K to 60 K, the specific resistance decreases in copper due to reduced thermal agitation and increases in silicon because of reduced carrier concentration.