Particle sizing — what distribution does microscopic analysis yield? When particle size is determined by direct microscopic counting and measurement, which type of size distribution is obtained?

Introduction / Context:
Different sizing methods yield different statistical weightings (number-, length-, area-, or volume-weighted). Understanding which distribution a method produces is crucial for comparing datasets and interpreting results in powder technology.

Given Data / Assumptions:

• Microscopic analysis counts and sizes individual particles on a field.
• All particles observed have equal “voting weight” as counts unless corrected.

Concept / Approach:
Direct microscopy produces a number-weighted distribution by default because each particle contributes one count regardless of its size. Other methods (e.g., sieving or sedimentation) often correlate more closely with mass/volume-weighted distributions.

Step-by-Step Solution:
Identify that counting at the microscope increments a tally per particle.Therefore the underlying weighting is by number of particles.Select “number” distribution.

Verification / Alternative check:
Standard texts classify: microscopy → number distribution; laser diffraction → volume distribution; sieving → mass (weight) distribution.

Why Other Options Are Wrong:

• Length/area/volume: these weight larger particles more heavily; not the default outcome of simple counting without special weighting corrections.

Common Pitfalls:

• Comparing number-based D50 with volume-based D50; they are not directly interchangeable.

Final Answer:
number