UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper III
Q1(a). Sample mass for a sampling standard deviation of ±5 %
Question
From the following data, determine the mass of the sample that should be analyzed to obtain sampling standard deviation of ±5 %. Given data: sample mass (g) 0.1, 1.5, 9.2; relative standard deviation (%) 15, 6, 2.5.
Answer in brief
Ks ≈ 45 g, so w = Ks/R² ≈ 1.8 g. Take about 2 g of sample.
Key points
- Sampling variance is inversely proportional to the sample mass: wR² = Ks (Ingamells sampling constant).
- Ks from each result: 0.1 × 15² = 22.5 g, 1.5 × 6² = 54.0 g, 9.2 × 2.5² = 57.5 g; mean Ks = 44.7 g.
- For R = 5 %: w = Ks/R² = 44.7/5² = 1.8 g.
- The two larger samples alone give Ks ≈ 56 g and w ≈ 2.2 g, so about 2 g is the safe working mass.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coverssampling errorIngamells sampling constantminimum sample sizerelative standard deviation
All parts of Question 1
- 1(a) Sample mass for a sampling standard deviation of ±5 %5 marks
- 1(b) van Deemter equation and its significance5 marks
- 1(c) Non-absorbing analyte by UV-vis spectrophotometry5 marks
- 1(d) Flame absorption profiles of magnesium and silver5 marks
- 1(e) Heating rate, particle size and heat of reaction in TGA5 marks
- 1(f) Quadrupole mass analyser in ICP–MS5 marks
- 1(g) Gravimetric estimation of nickel in steel5 marks
- 1(h) Lattice spacing from Bragg’s law5 marks