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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper I covers inorganic chemistry.

UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper I

Q9(a). Isotope dilution method

  • 10 marks
  • Topic: Radiochemical analysis
  • Answered
Question

How is isotope dilution method used to determine the amount of an element present in a sample?

Answer in brief

A known mass m₀ of the element labelled with a radioisotope (specific activity S₀) is mixed with the sample. After complete mixing a small, pure portion is isolated (not quantitatively) and its specific activity S is measured. The unknown mass is x=m₀((S₀)/(S)-1).

Key points

  • the radioactive tracer is diluted by the inactive element of the sample; the fall in specific activity gives the mass of the inactive element.
  • activity of the tracer A₀=S₀m₀ is conserved on mixing. After mixing the total mass is m₀+x, so S=(A₀)/(m₀+x)=(S₀m₀)/(m₀+x) ⇒ x=m₀((S₀)/(S)-1) (S=activity per unit mass of the isolated pure element)
  • (a) prepare the tracer of known m₀, S₀; (b) add and equilibrate (chemical exchange, dissolution); (c) separate any pure fraction (precipitate, extract, crystallise) of mass mₛ; (d) count its activity Aₛ in a GM or…
  • 10.0 mg of ⁵⁹Fe-labelled iron (S₀=2000 counts min⁻¹ mg⁻¹) is added to an iron ore solution. 5.0 mg of pure iron isolated has 1.00×10³ counts min⁻¹, so S=200: x=10.0((2000)/(200)-1)=90 mg.

The full model answer

Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.

  1. Principle: the radioactive tracer is diluted by the inactive element of the sample; the fall in specific activity gives the mass of the inactive element.
  2. Derivation: activity of the tracer A₀=S₀m₀ is conserved on mixing. After mixing the total mass is m₀+x, so S=(A₀)/(m₀+x)=(S₀m₀)/(m₀+x) ⇒ x=m₀((S₀)/(S)-1) (S=activity per unit mass of the isolated pure element)
  3. Steps: (a) prepare the tracer of known m₀, S₀; (b) add and equilibrate (chemical exchange, dissolution); (c) separate any pure fraction (precipitate, extract, crystallise) of mass mₛ; (d) count its activity Aₛ in a GM or scintillation counter; S=Aₛ/mₛ; (e) calculate x.
  4. Example: 10.0 mg of ⁵⁹Fe-labelled iron (S₀=2000 counts min⁻¹ mg⁻¹) is added to an iron ore solution. 5.0 mg of pure iron isolated has 1.00×10³ counts min⁻¹, so S=200: x=10.0((2000)/(200)-1)=90 mg.
  5. Advantages: no need for quantitative separation; yield losses do not matter because S is a ratio; high sensitivity (traces, μg); applicable to complex matrices (blood volume with ¹³¹I-albumin, Zn in biological samples).
  6. Limits: needs a suitable isotope of long enough half-life; complete isotopic exchange; radiation safety.

if a non-radioactive stable isotope is used (¹³C, ¹⁵N) and measured by mass spectrometry, it is called isotope-dilution mass spectrometry, the reference method for trace elements in geochemical standards.

Model answer to Q9(a), 2026 Mains Paper I: solution page 19
Solution page 19 of 26
Read the whole 2026 solution2026 question paper

Coversisotope dilutionIsotope dilution method

All parts of Question 9