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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

Q1(h). Radioactive displacement: ²¹⁰Pb and ²²⁶Ra

  • 5 marks
  • Topic: Nuclear chemistry
  • Answered
Question

Find the values of a and b in the following reactions of radioactivity: (i) ²¹⁰₈₂Pb →ᵃ_bX (ii) ²²⁶₈₈Ra →ᵃ_bY. Predict the position of the daughter element in the periodic table.

Answer in brief

(i) a=210, b=83 (Bi, group 15, period 6). (ii) a=222, b=86 (Rn, group 18, period 6).

Key points

  • β⁻ emission: a neutron becomes a proton: A unchanged, Z+1. ²¹⁰₈₂Pb → ²¹⁰₈₃Bi + e⁻ (plus an antineutrino). Bi is one group to the right of Pb: Pb (14) → Bi (15).
  • α emission: ⁴₂He is lost: A-4, Z-2. ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Rn is two groups to the left of Ra: Ra (2) → Rn (18, previous period's noble gas).
  • mass number 210=210+0; 226=222+4; charge 82=83-1; 88=86+2.

The full model answer

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

  • β⁻ emission: a neutron becomes a proton: A unchanged, Z+1. ²¹⁰₈₂Pb → ²¹⁰₈₃Bi + e⁻ (plus an antineutrino). Bi is one group to the right of Pb: Pb (14) → Bi (15).
  • α emission: ⁴₂He is lost: A-4, Z-2. ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He. Rn is two groups to the left of Ra: Ra (2) → Rn (18, previous period's noble gas).
  • Check: mass number 210=210+0; 226=222+4; charge 82=83-1; 88=86+2.

²¹⁰Pb (t_(1/2)=22.2 y) → ²¹⁰Bi → ²¹⁰Po is the basis of lead-210 dating of lake sediments and peat.

Model answer to Q1(h), 2026 Mains Paper I: solution page 6
Solution page 6 of 26
Read the whole 2026 solution2026 question paper

CoversSoddy–Fajans rulesRadioactive displacement²¹⁰Pb and ²²⁶Ra

All parts of Question 1