In mineral separation terminology, the “selectivity index” is defined as which of the following (consider two-mineral separation with relative rejections and recoveries)?

Introduction / Context:
Quantifying separation quality requires precise metrics. Selectivity index provides a measure that combines recovery and rejection performance, enabling comparison across operating conditions.

Given Data / Assumptions:

• Two-mineral system (valuable and gangue).
• Relative recovery and relative rejection are known.
• Definition requested is geometric mean of these relative measures.

Concept / Approach:
The selectivity index (sometimes called the “separating power”) is defined as the geometric mean of relative recovery of valuable in concentrate and relative rejection of gangue to tailings. This balances both aspects of separation in a single figure-of-merit. Separation efficiency and concentration ratio are different metrics and do not use this specific geometric mean definition.

Step-by-Step Solution:
Recall formal definitions of common separation indices.Match the geometric mean definition with selectivity index.Select “Selectivity index.”

Verification / Alternative check:
Standard mineral processing texts present the geometric mean form for selectivity, distinct from linear combinations used in separation efficiency.

Why Other Options Are Wrong:
Separation efficiency: combines recovery and purity differently (often linear).Concentration ratio: simple ratio of grades, not a geometric mean of relative metrics.None/Partition slope: not matching the stated definition.

Common Pitfalls:
Using only recovery to judge separation without considering rejection, which the selectivity index balances.

Final Answer:
Selectivity index