Question

Consider two cuboidal blocks of volume 1 cm\(^3\) each, one made of gold and the other of undoped silicon. What will happen to the resistivity of these blocks if the temperature is increased from 300 K to 350 K? Choose one of the following.

• A. Resistivity of gold increases and undoped silicon decreases
• B. Resistivity of gold decreases and undoped silicon increases
• C. Resistivity of gold remains same and undoped silicon increases
• D. Resistivity of gold decreases and undoped silicon remains same

Hint:

A simple rule to remember: For metals, Temperature \(\uparrow\) \(\implies\) Resistivity \(\uparrow\). For semiconductors, Temperature \(\uparrow\) \(\implies\) Resistivity \(\downarrow\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks about the effect of increasing temperature on the electrical resistivity of a metal (gold) and an intrinsic semiconductor (undoped silicon).
Step 2: Detailed Explanation:
The behavior of resistivity with temperature is fundamentally different for metals and semiconductors due to their different charge carrier mechanisms.

• Gold (a Metal): In metals, the concentration of free electrons (charge carriers) is very high and does not change significantly with temperature. Conduction is limited by the scattering of these electrons. As temperature increases, the metal ions in the lattice vibrate more intensely. These increased lattice vibrations (phonons) scatter the moving electrons more frequently, impeding their flow. This increased scattering leads to an increase in resistivity.
  
• Undoped Silicon (a Semiconductor): In an intrinsic semiconductor, the number of charge carriers (electrons in the conduction band and holes in the valence band) is relatively low at room temperature. As temperature increases, thermal energy excites more electrons from the valence band across the band gap to the conduction band. This process creates more electron-hole pairs, significantly increasing the concentration of charge carriers. This increase in carrier density is the dominant effect and outweighs the increased scattering effect. A higher number of charge carriers leads to better conductivity, which means the resistivity decreases.
  

Step 3: Final Answer:
Therefore, as the temperature increases, the resistivity of gold will increase, and the resistivity of undoped silicon will decrease.