Magnetic properties of diamond: Evaluate the assertion–reason pair—Assertion (A) For diamond, μ_r = 1. Reason (R) Diamond is a diamagnetic material.
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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 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 false but R is true
Explanation
Introduction / Context:Magnetic materials are characterized by susceptibility χ and relative permeability μ_r = 1 + χ. Diamagnetic materials have small negative χ, leading to μ_r slightly less than 1. Diamond, an sp^3-bonded carbon crystal, is strongly covalent and exhibits diamagnetism with very small magnitude.
Given Data / Assumptions:
- Assertion claims μ_r equals exactly 1 for diamond.
- Reason states that diamond is diamagnetic.
Concept / Approach:
Because diamond is diamagnetic (χ < 0 but |χ| ≪ 1), its μ_r is close to but not exactly 1 (μ_r = 1 + χ < 1). Thus the assertion is strictly false, while the reason is true. The reason does not support the assertion; if anything, it contradicts it by implying μ_r is slightly less than 1.
Step-by-Step Solution:
Use μ_r = 1 + χ.For diamagnetic diamond, χ is small and negative ⇒ μ_r ≈ 1 − |χ| < 1.Therefore A false, R true.Verification / Alternative check:
Measured susceptibilities of many diamagnetic insulators are on the order of 10^-6 to 10^-5 (negative), confirming μ_r is slightly below 1.
Why Other Options Are Wrong:
- Any option implying A true is inconsistent with the definition μ_r = 1 + χ and χ < 0 for diamagnetics.
Common Pitfalls:
- Rounding μ_r to 1 for convenience; exact statements should distinguish “≈1” from “=1”.
Final Answer:
A is false but R is true