JEE Main 2023 · 29 January · morning · Single correct · +4 / −1

If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be

  1. (a) 1/16
  2. (b) 1/4
  3. (c) 1/8
  4. (d) 1/2
Answer and solution

Answer (c) 1/8

Solution

Physics sir · 3 steps

Count the half-lives first: 90 minutes is exactly three half-lives of 30 minutes each.

  1. Number of half-lives. Divide the time elapsed by the half-life: n = (90 min)/(30 min) = 3.

    N/N₀ = (1/2)ⁿ = (1/2)³ = 1/8

  2. Check step by step. After 30 min, 1/2 is left. After 60 min, 1/4 is left. After 90 min, 1/8 is left. The type of decay (beta here) does not change this rule.
  3. So. The fraction that remains undecayed after 90 min is 1/8, option (c).

The idea to keep. For any radioactive decay, the fraction left after n half-lives is (1/2)ⁿ. Find n = t/T_(1/2) first, then halve that many times.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 110 times in JEE Main since 2020. This question is from 2023.