Radioactive decay – JEE First

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 $\ln 10 = 2.3$ ],

1.15
9.2
2.3
4.6

Solution

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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Radioactive decay of Potassium