Testing the hardness of a mineral, you notice that it is scratched by quartz but not by orthoclase. The approximate hardness of this mineral is:

Question

Testing the hardness of a mineral, you notice that it is scratched by quartz but not by orthoclase.  The approximate hardness of this mineral is:

BlackTom AI · Accepted Answer

On the Mohs hardness scale, orthoclase (a feldspar) is hardness 6 and quartz is hardness 7. That scale is ordinal: a mineral that is scratched by another must be softer (have a lower Mohs number) than the one doing the scratching.

1) Relevant concepts:
- Mohs hardness: comparative ordinal scale where higher numbers scratch lower numbers (orthoclase = 6, quartz = 7).
- If material A scratches B, hardnessA > hardnessB. If A does not scratch B, then hardnessA ≤ hardnessB (equal hardness generally produces no clear scratch).

2) Step-by-step reasoning:
- The mineral is scratched by quartz (hardness 7). Therefore hardness(mineral) < 7.
- The mineral is not scratched by orthoclase (hardness 6). Therefore hardness(orthoclase) ≤ hardness(mineral), so hardness(mineral) ≥ 6.
- Combine the two inequalities: 6 ≤ hardness(mineral) < 7.

3) Intermediate “calculation” (inequality work):
- From quartz scratching: H < 7.
- From orthoclase not scratching: 6 ≤ H.
- Combine: 6 ≤ H < 7 → approximate range 6–7 on Mohs scale.

4) Why the correct answer is correct:
Because the mineral lies between orthoclase and quartz in hardness: orthoclase cannot scratch it (so it is at least as hard as 6) but quartz can scratch it (so it is softer than 7). That places it in the 6–7 interval.

5) Why other options are incorrect:
- 8–9: If hardness were 8–9, quartz (7) would not be able to scratch it, contradicting the observation.
- 1–2: If hardness were 1–2, orthoclase (6) would certainly scratch it, contradicting “not scratched by orthoclase.”
- 10–11: Mohs scale nominally runs 1–10; a value ≥10 would also contradict being scratched by quartz (7).

6) Conclusion:
The mineral’s approximate hardness is 6–7, which matches the provided correct answer.

Testing the hardness of a mineral, you notice that it is scratched by quartz but not by orthoclase. The approximate hardness of this mineral is:单项选择题

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