Assertion–Reason: (A) The conductivity of a p-type semiconductor is higher than that of an intrinsic semiconductor. (R) Adding donor impurities creates extra energy levels just below the conduction band.
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ABoth A and R are true and R is correct explanation of A
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BBoth A and R are true but R is not a correct explanation of A
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CA is true but R is false
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DA is false but R is true
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EBoth A and R are false
Answer
Correct Answer: A is true but R is false
Explanation
Introduction / Context:Assertion–Reason questions evaluate not only factual correctness but also causal linkage. Here we compare conductivity of p-type versus intrinsic material and examine whether the stated reason logically supports the assertion.
Given Data / Assumptions:
- Intrinsic semiconductor: n = p = ni; conductivity σi = q ni (μn + μp).
- p-type semiconductor: majority holes with p ≫ n; conductivity σp ≈ q p μp with p set by acceptor doping.
- Donor impurities (n-type) introduce energy levels near the conduction band; acceptor impurities (p-type) introduce levels near the valence band.
Concept / Approach:The assertion states p-type conductivity exceeds intrinsic conductivity—usually true, because doping greatly increases majority carrier concentration compared to ni at room temperature. The reason, however, mentions donor impurities (n-type mechanism) rather than acceptors, so it does not explain the improved conductivity of a p-type semiconductor. Thus A is true, R is false in this context.
Step-by-Step Solution:
Assess A: Doping (acceptors) raises hole concentration well above ni → σ increases → A is true.Assess R: Donor levels below conduction band correspond to n-type doping, irrelevant to p-type improvement → R is false as an explanation for A.Therefore, correct choice: A true, R false.Verification / Alternative check:
If R had referred to acceptor levels near the valence band (promoting holes), it could have explained A. Since it does not, the pairing fails.Why Other Options Are Wrong:
(a) Incorrect because R does not support A.(b) R is not even true in the p-type context used to explain A.(d) A is not false; p-type typically has higher σ than intrinsic.Common Pitfalls:
Overlooking the specific impurity type (donor vs acceptor) in reason statements.Final Answer:
A is true but R is false