Assertion–Reason on hardness of diamond and carborundum (silicon carbide) Assertion (A): Diamond and carborundum (silicon carbide) are both very hard materials. Reason (R): The valence band can be extremely strong.
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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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ENeither A nor R is true
Answer
Correct Answer: A is true but R is false
Explanation
Introduction / Context:Hardness in covalent solids is governed by chemical bonding geometry and bond strength, not by abstract band-structure labels alone. Diamond and silicon carbide are classic superhard materials due to strong directional covalent bonds in robust 3D networks.
Given Data / Assumptions:
- Materials: diamond (sp^3-bonded carbon) and carborundum (SiC).
- Room-temperature mechanical hardness considered.
- Ideal, defect-minimized crystals.
Concept / Approach:Hardness correlates with strong covalent bonding and dense, rigid crystal frameworks. In diamond, each carbon forms four short, strong sp^3 bonds in a tetrahedral network. In SiC, strong Si–C covalent bonds form a similarly stiff lattice. The phrasing “valence band can be extremely strong” is incorrect; bands describe electronic energy levels, not a mechanical entity. The correct explanation involves strong valence bonds, not “valence band.”
Step-by-Step Solution:Assess Assertion: diamond and SiC are indeed very hard → true.Assess Reason: “valence band is strong” is a category error; mechanical hardness stems from strong covalent bonds and bonding topology.Conclusion: A true; R false.
Verification / Alternative check:Experimental hardness scales (Vickers/Knoop) rank diamond at the top; SiC is also classified as superhard/ultrahard. Ab initio calculations tie stiffness to covalent bond strength and bulk/shear moduli, not band strength.
Why Other Options Are Wrong:(a) suggests R correctly explains A, but it does not. (b) keeps both true, which is wrong since R is false. (d) negates A, contradicting data. (e) is incorrect because A is true.
Common Pitfalls:
- Confusing “band” (electronic energy concept) with “bond” (chemical linkage).
- Ignoring the role of 3D network connectivity and short bond length in hardness.
Final Answer:A is true but R is false