Metallic conductors and semiconductors are heated separately. What are the changes in conductivity?

Question

The molar conductances of Ba(OH)$_2$, BaCl$_2$ and NH$_4$Cl at infinite dilution are 523.28, 280.0 and 129.8 S cm$^2$ mol$^{-1$ respectively. The molar conductance of NH$_4$OH at infinite dilution will be:}

Answer 1

Heating metallic conductors and semiconductors affects their conductivity differently because of their different structures and how they conduct electricity.

Metallic Conductors:

Metals' conductivity depends on how many free electrons they have and how easily those electrons can move. When heated, metal atoms vibrate more. This causes free electrons to collide more often with the atoms, making it harder for them to move. Conductivity ($\sigma$) relates directly to the number of free electrons ($n$), the elementary charge ($e$), and electron mobility ($\mu$), and inversely to the relaxation time ($\tau$):

$\sigma = n e \mu $ or $\sigma \propto \frac{1}{\tau}$

As temperature goes up, $\tau$ goes down because of more collisions, which causes conductivity to decrease. The number of free electrons in metals stays about the same with temperature changes.

Semiconductors:

In semiconductors, conductivity is strongly affected by the number of charge carriers (electrons and holes). At lower temperatures, there are fewer charge carriers. When heated, more electrons get enough energy to jump from the valence band to the conduction band, creating more free electrons and holes (intrinsic carrier generation).

Semiconductor conductivity increases exponentially with temperature, approximated by:

$\sigma = \sigma_0 e^{-\frac{E_g}{2kT}}$

Where:

$\sigma_0$ is a constant,

$E_g$ is the band gap energy,

$k$ is the Boltzmann constant, and

$T$ is the absolute temperature.

As temperature rises, the exponential term increases, leading to a significant increase in conductivity. Even though carrier mobility might slightly decrease, the increase in carrier concentration is the main factor in conductivity.

Conclusion:

Therefore, heating metallic conductors causes their conductivity to decrease, while heating semiconductors causes their conductivity to increase.

Correct Answer: Decrease, Increase

Metallic conductors and semiconductors are heated separately. What are the changes in conductivity?

The Correct Option is D

Solution and Explanation

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