Assertion: The number of electrons in a `p`-type silicon semiconductor is less than the number of electrons ina pure silicon semiconductor at room temperature.
Reason: It is due to law of mass action.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Understand the Assertion
The assertion states that "the number of electrons in a `p`-type silicon semiconductor is less than the number of electrons in a pure silicon semiconductor at room temperature."

- In a pure silicon semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band, as they are generated in pairs when thermal energy excites electrons.
- In a `p`-type semiconductor, which is doped with acceptor impurities (like boron), there are more holes than electrons. The acceptor atoms create holes by accepting electrons from the valence band, which reduces the number of free electrons.

**Conclusion for Step 1**: The assertion is **true** because the presence of acceptor impurities in `p`-type silicon leads to a decrease in the number of free electrons compared to pure silicon.

### Step 2: Understand the Reason
The reason states that "it is due to the law of mass action."

- The law of mass action in semiconductors states that the product of the concentration of electrons (n) and holes (p) in intrinsic semiconductors remains constant at a given temperature. This can be expressed as \( n \cdot p = n_i^2 \), where \( n_i \) is the intrinsic carrier concentration.
- In a `p`-type semiconductor, as the number of holes (p) increases due to doping, the number of electrons (n) must decrease to maintain the product \( n \cdot p \) constant.

**Conclusion for Step 2**: The reason is **true** because the law of mass action explains the relationship between the number of holes and electrons in semiconductors.

### Final Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer
Both the assertion and the reason are true, and the reason correctly explains the assertion.