Extrinsic semiconductor doping level and effect (assertion–reason) Assertion (A): Doping levels in extrinsic semiconductors are extremely small fractions of the host atoms. Reason (R): Adding impurity atoms at a ratio of about 1 in 10^8 parts can increase the number of charge carriers by roughly 20 times.

Introduction / Context:
Doping transforms intrinsic semiconductors into n- or p-type extrinsic materials by introducing donors or acceptors at extremely low atomic fractions. Even minute dopant concentrations radically change carrier density and conductivity. This assertion–reason item probes both the qualitative smallness of doping and the quantitative impact on carriers.

Given Data / Assumptions:

• Host atomic density for Si ≈ 5×10^22 atoms/cm^3 (order of magnitude).
• Intrinsic carrier concentration at 300 K: ni ≈ 10^10 cm^−3 for Si.
• Typical dopings: 10^13–10^18 cm^−3, i.e., atomic fractions as low as 10^−10 to 10^−4.

Concept / Approach:

Assertion: True. The fraction of dopant atoms is tiny relative to host atoms, yet it dominates electrical properties. Reason: False as stated. A ratio of 1 in 10^8 corresponds to about 5×10^14 cm^−3 in Si, which exceeds ni by roughly 10^4–10^5, not merely “about 20”. Thus the numerical claim understates the effect by many orders of magnitude. Although the spirit that “very little dopant makes a big difference” is correct, the stated factor of ~20 is inaccurate.

Step-by-Step Solution:

Verification / Alternative check:

Device textbooks show conductivity changing by many orders of magnitude when moving from intrinsic to doped silicon even at ppm–ppb dopant levels.

Why Other Options Are Wrong:

Any option treating R as true or as a correct explanation of A conflicts with the realistic numbers for silicon at room temperature.

Common Pitfalls:

Confusing fractional dopant level with fractional change in carriers; the former can be tiny while the latter is huge.

Final Answer:

A is true but R is false