Assertion (A): The number of electrons in a p-type silicon semiconductor is less than the number of electrons in intrinsic silicon semiconductor at room temperature.
Reason (R ): It is due to law of mass action.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Explanation

To solve the question, we will analyze the assertion and the reason provided, and then conclude whether they are true or false, as well as whether the reason correctly explains the assertion.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "The number of electrons in a p-type silicon semiconductor is less than the number of electrons in intrinsic silicon semiconductor at room temperature."
- In intrinsic silicon, the number of electrons (n_i) is equal to the number of holes (p_i) at thermal equilibrium. At room temperature, this is a balanced state.
- In a p-type semiconductor, which is created by doping silicon with trivalent elements (like Boron), there are more holes than electrons. This means that the number of free electrons available in p-type silicon is indeed less than in intrinsic silicon.

2. **Understanding the Reason (R)**:
- The reason states that "It is due to law of mass action."
- The law of mass action in semiconductors states that the product of the concentration of electrons (n) and holes (p) is constant at a given temperature, which can be expressed as:
\[ n_i^2 = n \cdot p \]
- In a p-type semiconductor, since the concentration of holes (p) is increased due to doping, the concentration of electrons (n) must decrease to maintain this product constant. Thus, the law of mass action supports the assertion.

3. **Conclusion**:
- Since both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion, we can conclude that both statements are valid and interconnected.

### Final Answer:
Both the assertion (A) and the reason (R) are true, and the reason is the correct explanation for the assertion.

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