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In which of the following the conductivi...

In which of the following the conductivity would be in the order of `10^(-4) ohm^(-1)cm^(-1)`

A

`NaCl_((s))`

B

`Na_((s))`

C

Diamond

D

`Ge`

Text Solution

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The correct Answer is:
To determine which of the given materials has a conductivity in the order of \(10^{-4} \, \text{ohm}^{-1}\text{cm}^{-1}\), we need to analyze the conductivity ranges of conductors, insulators, and semiconductors. ### Step-by-Step Solution: 1. **Understanding Conductivity**: - Conductivity (\(\sigma\)) is a measure of a material's ability to conduct electric current. It is the inverse of resistivity (\(\rho\)). - The general relationship is given by: \[ \sigma = \frac{1}{\rho} \] 2. **Conductivity Ranges**: - **Conductors**: Have high conductivity, typically in the range of \(10^2\) to \(10^8 \, \text{ohm}^{-1}\text{cm}^{-1}\). - **Insulators**: Have very low conductivity, usually around \(10^{-11} \, \text{ohm}^{-1}\text{cm}^{-1}\) or lower. - **Semiconductors**: Have intermediate conductivity, generally in the range of \(10^{-5}\) to \(10^{6} \, \text{ohm}^{-1}\text{cm}^{-1}\). 3. **Analyzing the Options**: - We need to find a material whose conductivity falls within the range of \(10^{-4} \, \text{ohm}^{-1}\text{cm}^{-1}\). - From the ranges established: - Conductors are too high. - Insulators are too low. - Semiconductors can potentially fit this range. 4. **Identifying Specific Materials**: - **NaCl (Sodium Chloride)**: As an ionic solid, it acts as an insulator in solid state, thus having low conductivity. - **Sodium Metal**: A good conductor, with conductivity much higher than \(10^{-4} \, \text{ohm}^{-1}\text{cm}^{-1}\). - **Diamond**: A non-metallic solid with no free charge carriers, thus it acts as an insulator. - **Germanium**: A semiconductor, which typically has conductivity in the range of \(10^{-5}\) to \(10^{-6} \, \text{ohm}^{-1}\text{cm}^{-1}\), making it a candidate for our required range. 5. **Conclusion**: - The material that fits the conductivity order of \(10^{-4} \, \text{ohm}^{-1}\text{cm}^{-1}\) is **Germanium**, which is a semiconductor. ### Final Answer: The correct answer is **Germanium**.
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