Radioactive decay of Potassium

JEE Advanced 2019 Paper 1, Question 4

In a radioactive sample, {}^{40}_{19}{\rm K} nuclei decay into stable {}^{40}_{20}{\rm Ca} nuclei with decay constant 4.5 \times 10^{-10} per year or into stable {}^{40}_{18}{\rm Ar} nuclei with decay constant 0.5 \times 10^{-10} per year. In this sample all the stable {}^{40}_{20}{\rm Ca} and {}^{40}_{18}{\rm Ar} nuclei are produced by the {}^{40}_{19}{\rm K} nuclei only. In time t_1 \times 10^9 years, if the ratio of the sum of stable {}^{40}_{20}{\rm Ca} and {}^{40}_{18}{\rm Ar} nuclei to the radioactive {}^{40}_{19}{\rm K} nuclei is 99, the value of t_1 will be [Given \ln 10 = 2.3],

  1. 1.15
  2. 9.2
  3. 2.3
  4. 4.6


Let us first consider the situation where a sample of X nuclei decays into a single type of nuclei Y. The number N of X nuclei changes with …

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