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Chapter 19: Problem 2606

The number of holes and electrons in an intrinsic conductors are \(\mathrm{x}\) and \(\mathrm{y}\) respectively at room temperature. Which of the following options are true? (A) \(x>y\) (B) \(\mathrm{y}>\mathrm{x}\) (C) \(x=y\) (D) \(x<

Short Answer

Expert verified
In an intrinsic conductor at room temperature, the number of holes (x) and electrons (y) are equal due to the equilibrium conditions. Thus, the correct relationship is \(x = y\), making option (C) the true statement.

Step by step solution

01

Understand intrinsic conductors

Intrinsic conductors are pure semiconductor materials with no impurities. At room temperature, they have a nearly equal balance of electrons and holes, the charge carriers responsible for electrical conductivity.
02

Equilibrium conditions

At room temperature, an intrinsic conductor is in equilibrium, which means that the rate of generation and recombination of charge carriers are equal. This balance results in equal concentrations of electrons and holes in the material.
03

Determine the relationship between x and y

Since intrinsic conductors have equal concentrations of electrons and holes in equilibrium at room temperature, we can state that the number of electrons (y) is equal to the number of holes (x). Therefore, the correct relationship is: \(x = y\). Now we can identify which of the given options is true.
04

Select the correct option

After determining that the relationship between x and y is \(x = y\), we can identify option (C) as the correct answer: (C) x=y

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