Among the following minerals, which one has the minimum Rittinger’s number (i.e., requires the least energy per unit new surface area created) under comparable conditions?

Introduction / Context:
Rittinger’s number reflects the energy needed to create unit new surface. Softer, cleavage-prone minerals typically show lower values than hard, tough minerals.

Given Data / Assumptions:

• Minerals listed: calcite, pyrite, quartz, galena.
• Measurements compared at similar size ranges and conditions.

Concept / Approach:
Quartz is very hard and tough, implying a high Rittinger’s number. Pyrite and calcite are moderate; galena (lead sulfide) is very soft and exhibits perfect cleavage, making surface generation easier and energy per area lower, hence a smaller Rittinger’s number.

Step-by-Step Solution:
Rank by hardness/toughness: quartz > pyrite ≈ calcite > galena.Associate lower hardness/cleavage with lower energy per area.Select galena as minimum.

Verification / Alternative check:
Grinding practice shows galena liberates readily with less power compared with quartz-bearing ores.

Why Other Options Are Wrong:
Quartz: very high energy per surface created.Pyrite/Calcite: higher than galena though lower than quartz.

Common Pitfalls:
Equating Mohs hardness linearly with grindability; cleavage also matters.

Final Answer:
Galena