Question

The values of conductivity of some materials at \( 298.15 \, \text{K} \) in \( \text{S m}^{-1} \) are:
\( 2.1 \times 10^3, \, 1.0 \times 10^{-16}, \, 1.2 \times 10^1, \, 3.91, \, 1.5 \times 10^{-2}, \, 1 \times 10^{-7}, \, 1.0 \times 10^3 \).
The number of conductors among the materials is ______.

Answer 1

Correct Answer: 4

The conductivity of a material indicates its ability to conduct electricity. Materials with high conductivity are categorized as conductors. For this analysis, a standard threshold is needed: materials with conductivities significantly greater than \( 1 \, \text{S m}^{-1} \) are typically considered conductors. Let's evaluate each given material based on this criteria.

1. \( 2.1 \times 10^3 \) is greater than \( 1 \, \text{S m}^{-1} \), thus it is a conductor.
2. \( 1.0 \times 10^{-16} \) is much less than \( 1 \, \text{S m}^{-1} \), therefore, it is not a conductor.
3. \( 1.2 \times 10^1 = 12 \), which is greater than \( 1 \, \text{S m}^{-1} \), so it is a conductor.
4. \( 3.91 \) is greater than \( 1 \, \text{S m}^{-1} \), indicating it is a conductor.
5. \( 1.5 \times 10^{-2} = 0.015 \), which is less than \( 1 \, \text{S m}^{-1} \). Thus, it is not a conductor.
6. \( 1 \times 10^{-7} = 0.0000001 \), also less than \( 1 \, \text{S m}^{-1} \), making it not a conductor.
7. \( 1.0 \times 10^3 = 1000 \), which is greater than \( 1 \, \text{S m}^{-1} \), hence it is a conductor.

Counting the number of materials with conductivity greater than \( 1 \, \text{S m}^{-1} \), we find 4 conductors:

• \( 2.1 \times 10^3 \)
• \( 1.2 \times 10^1 \)
• \( 3.91 \)
• \( 1.0 \times 10^3 \)

The number of conductors is thus 4, which matches the expected range (4).

Answer 2

The materials can be categorized as conductors, insulators, and semiconductors based on their conductivity values at 298.15 K.

Conductors generally have conductivities on the order of \(10^2\) to \(10^6 \, \text{S m}^{-1}\).
Insulators have very low conductivities, typically around \(10^{-10}\) to \(10^{-8} \, \text{S m}^{-1}\).
Semiconductors have conductivities ranging from \(10^{-4}\) to \(10 \, \text{S m}^{-1}\).

Given values:

\[ 2.1 \times 10^3, \, 1.2 \times 10^3, \, 3.91, \, 1.5 \times 10^{-2}, \, 1 \times 10^{-7}, \, 1.0 \times 10^3 \]

Classifying each:

• \(2.1 \times 10^3, \, 1.2 \times 10^3, \, \text{and} \, 1.0 \times 10^3\) are in the conductor range.
• \(3.91\) also falls within the conductor range (upper range of semiconductors).
• \(1.5 \times 10^{-2}\) represents a semiconductor.
• \(1 \times 10^{-7}\) represents an insulator.

Therefore, the number of conductors is: 4.