VKC ScienceChemistry for written exams Telegram

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 · 2023 · Mains Paper I

Q1(h). Time for 74% radioactive material to remain

Question

A radioactive substance has a half-life of 250 years. How many years will it take to retain 74% of its original amount?

Answer in brief

Time required = 108.6 years, approximately 109 years.

Key points

  • Radioactive decay follows N/N₀ = e−λt, with λ = ln 2/t₁/₂.
  • The fraction remaining is 0.74, not 0.26; hence t = (t₁/₂/ln 2) ln(N₀/N).
  • Substitute: t = (250/0.693147) ln(1/0.74) = 108.60 years.
  • Since 74% is greater than 50%, the result must be less than one half-life, consistent with 108.6 < 250 years.

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.

Model answer to Q1(h), 2023 Mains Paper I: solution pages 9 and 10
Solution pages 9 and 10 of 26
Read the whole 2023 solution2023 question paper

Topic notes: nuclear chemistry: radioactive decay, binding energy, radiocarbon dating and the GM counter, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversradioactive decayhalf-lifefirst-order decaydecay constant

All parts of Question 1