Number and weight distribution of particles is a core pharmaceutics topic that explains how particle populations are described by count (number-based) and by mass or volume (weight-based) measures. B. Pharm students must master concepts like number distribution, weight (volume) distribution, D[3,2] surface mean, D[4,3] volume mean, mass median diameter (MMD), span, polydispersity, and measurement techniques (sieve analysis, laser diffraction, microscopy, cascade impactors). Understanding number-to-weight conversions, the d^3 dependence of mass, and implications for dissolution, content uniformity, and aerosol deposition is essential for formulation and quality control. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What primarily distinguishes number distribution from weight (volume) distribution?
- Number distribution counts particles; weight distribution accounts for particle mass or volume
- Number distribution measures particle mass; weight distribution counts particles
- They are identical for polydisperse samples
- Number distribution is only used for liquids
Correct Answer: Number distribution counts particles; weight distribution accounts for particle mass or volume
Q2. Which mean is commonly referred to as the mass (volume) moment mean and is dominated by larger particles?
- D[3,2] surface mean
- D[4,3] volume (mass) mean
- Number median diameter
- Geometric mean diameter
Correct Answer: D[4,3] volume (mass) mean
Q3. Which parameter represents the surface area–weighted mean diameter useful for processes dependent on surface area?
- D[4,3]
- D[3,2]
- Mass median diameter (MMD)
- Number density
Correct Answer: D[3,2]
Q4. For spherical particles of equal number, how does mass compare between 1 μm and 10 μm particles?
- Mass is equal for both sizes
- 10 μm particles have 10 times the mass
- 10 μm particles have 1000 times the mass
- 1 μm particles have greater mass
Correct Answer: 10 μm particles have 1000 times the mass
Q5. Which technique typically reports particle size as a volume-based distribution rather than a number-based distribution?
- Optical microscopy with manual counting
- Laser diffraction
- Particle counting by hemocytometer
- Gravimetric sieve count (number of particles)
Correct Answer: Laser diffraction
Q6. The mathematical reason weight distribution emphasizes larger particles is because particle mass scales approximately with which power of diameter for spheres?
- d^1
- d^2
- d^3
- d^4
Correct Answer: d^3
Q7. What does Dv(50) or D[4,3] median (often written D50) commonly indicate?
- The diameter below which 50% of the number of particles lies
- The diameter below which 50% of the volume or mass lies
- The arithmetic mean diameter
- The smallest detected particle diameter
Correct Answer: The diameter below which 50% of the volume or mass lies
Q8. What is the number median diameter?
- Diameter below which 50% of particle count lies
- Diameter below which 50% of mass lies
- Mean surface area diameter
- Mass median aerodynamic diameter
Correct Answer: Diameter below which 50% of particle count lies
Q9. Dv(90) in a volume-based distribution refers to:
- The diameter at which 90% of particles by number are smaller
- The diameter at which 90% of the volume (mass) is contained in smaller particles
- The mean of the top 10% largest particles by count
- The diameter of the largest particle measured
Correct Answer: The diameter at which 90% of the volume (mass) is contained in smaller particles
Q10. The span of a particle size distribution is calculated as (D90 − D10)/D50. What does a larger span indicate?
- Narrower, more uniform size distribution
- Wider, more polydisperse distribution
- Higher particle density
- Greater chemical purity
Correct Answer: Wider, more polydisperse distribution
Q11. Which distribution parameter is most sensitive to the presence of a small number of very large particles?
- Number median diameter
- Surface area mean D[3,2]
- Volume mean D[4,3]
- Mode of number distribution
Correct Answer: Volume mean D[4,3]
Q12. Which parameter is most influenced by the abundance of fines (very small particles)?
- D[4,3]
- D[3,2]
- Mass median aerodynamic diameter
- Bulk density
Correct Answer: D[3,2]
Q13. When converting a number distribution to a weight distribution for spherical particles, what additional information is required?
- Particle color and refractive index
- Particle density and diameter for volume calculation
- Only the number fractions are sufficient
- Temperature and humidity only
Correct Answer: Particle density and diameter for volume calculation
Q14. Which instrument provides aerodynamic particle size distribution relevant for inhalation studies?
- Laser diffraction instrument
- Cascade impactor or aerodynamic particle sizer
- Optical microscope only
- Sieve shaker
Correct Answer: Cascade impactor or aerodynamic particle sizer
Q15. A Coulter counter measures particle size based on electrical sensing; it typically reports which type of distribution by default?
- Number distribution (counts)
- Mass distribution without conversion
- Only refractive index distribution
- Only aerodynamic diameter
Correct Answer: Number distribution (counts)
Q16. Which statement about laser diffraction data is correct?
- It directly measures particle number distribution
- It measures scattering to infer a volume-based distribution
- It cannot detect particles larger than 1 μm
- It gives chemical composition, not size
Correct Answer: It measures scattering to infer a volume-based distribution
Q17. How does aggregation or agglomeration affect number and weight distributions?
- Aggregation increases number counts without changing mass
- Aggregation reduces apparent number and shifts distributions toward larger equivalent diameters
- Aggregation has no effect on measured distributions
- Aggregation only affects color, not size
Correct Answer: Aggregation reduces apparent number and shifts distributions toward larger equivalent diameters
Q18. Why is understanding both number and weight distributions essential for dissolution behavior of solid dosage forms?
- Number distribution predicts chemical stability only
- Weight distribution predicts taste of the drug
- Surface-area-related dissolution depends on number/surface distributions while dose uniformity depends on mass distribution
- Only particle color matters for dissolution
Correct Answer: Surface-area-related dissolution depends on number/surface distributions while dose uniformity depends on mass distribution
Q19. For a bimodal mixture with many small particles and a few very large particles, which distribution will show the large particles more prominently?
- Number distribution
- Weight (volume) distribution
- Neither distribution will show large particles
- Only colorimetric analysis will show them
Correct Answer: Weight (volume) distribution
Q20. If the diameter of a spherical particle doubles, how does its mass change assuming constant density?
- Mass doubles
- Mass increases fourfold
- Mass increases eightfold
- Mass does not change
Correct Answer: Mass increases eightfold
Q21. Which measure is typically reported as mass median aerodynamic diameter (MMAD) in aerosol characterization?
- Number median aerodynamic diameter
- Mass median aerodynamic diameter (MMAD) — the diameter where 50% of mass is on smaller aerodynamic sizes
- Surface area median diameter
- Optical median diameter
Correct Answer: Mass median aerodynamic diameter (MMAD) — the diameter where 50% of mass is on smaller aerodynamic sizes
Q22. In practice, why might a formulator prefer reporting both number and weight distributions?
- The two reports are redundant and unnecessary
- Number distribution informs particle counts and surface area; weight distribution informs mass-related properties and dose uniformity
- Regulations require only one type, never both
- Because instruments always output both exactly the same
Correct Answer: Number distribution informs particle counts and surface area; weight distribution informs mass-related properties and dose uniformity
Q23. How does particle shape affect conversion between number and weight distributions?
- Shape has no effect if density is known
- Non-spherical shapes require shape factor or equivalent volume to convert accurately
- Only color influences conversion
- Shape only affects optical measurements, not conversions
Correct Answer: Non-spherical shapes require shape factor or equivalent volume to convert accurately
Q24. Which parameter best indicates broadness of a log-normal particle size distribution?
- Mode value alone
- Geometric standard deviation (GSD)
- Refractive index
- Bulk porosity
Correct Answer: Geometric standard deviation (GSD)
Q25. When calculating weight fraction from number fraction for spheres, the numerator of each size class contains n_i * d_i^3. What does n_i represent?
- Number of particles in class i
- Density of particles in class i
- Surface area of particles in class i
- Porosity of particles in class i
Correct Answer: Number of particles in class i
Q26. Which measurement is most appropriate for regulatory aerosol deposition studies in inhalation products?
- Sieve analysis
- Cascade impactor providing MMAD and geometric standard deviation
- Counting chamber for tablets
- Colorimetry
Correct Answer: Cascade impactor providing MMAD and geometric standard deviation
Q27. If a laser diffraction instrument reports D[4,3] = 50 µm and D[3,2] = 20 µm, what does this suggest about the sample?
- The sample is monodisperse
- The sample contains significant larger particles increasing the volume mean relative to the surface mean
- The sample is purely nanosized
- The instrument likely failed and produced random values
Correct Answer: The sample contains significant larger particles increasing the volume mean relative to the surface mean
Q28. Which instrument or method directly yields number-based size distributions from optical imaging?
- Laser diffraction without conversion
- Image analysis by microscopy with particle counting
- Sieve analysis reporting only mass fractions
- Cascade impactor reporting MMAD only
Correct Answer: Image analysis by microscopy with particle counting
Q29. How does increasing polydispersity typically affect blend uniformity in powder formulations?
- Higher polydispersity always improves uniformity
- Greater size differences can promote segregation and reduce content uniformity
- Polydispersity only affects color, not mixing
- Polydispersity has no impact if densities are identical
Correct Answer: Greater size differences can promote segregation and reduce content uniformity
Q30. Which statement about conversion from volume distribution to mass distribution is correct for materials of uniform density?
- Volume distribution cannot be converted to mass distribution even with known density
- Mass distribution equals volume distribution scaled by particle density, so for uniform density they are proportional
- Mass distribution is unrelated to volume when density is uniform
- Conversion requires optical rotation measurements
Correct Answer: Mass distribution equals volume distribution scaled by particle density, so for uniform density they are proportional
I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.
Mail- Sachin@pharmacyfreak.com