The half-life of ¹⁹⁸Au is 3 days. If atomic weight of ¹⁹⁸Au is 198 g/mol then the activity of 2 mg of ¹⁹⁸Au is [in disintegration/second]: (a) 2.67 × 1012 (b) 6.06 × 1018 (c) 32.36 × 1012 (d) 16.18 × 1012

Answer: (d). N = 2×10⁻³198×6.02×10²³ ≈ 6.08×10¹⁸. λ = (0.693)/(3×86400 s) ≈ 2.67×10⁻⁶ s⁻¹. A = λ N ≈ 1.62×10¹³ = 16.2×10¹² dis/s. So the answer is (d) 16.18×10¹².

The half-life of ¹⁹⁸Au is 3 days. If atomic weight of ¹⁹⁸Au is 198… | JEE Main 2021 (25 Jul, Shift 1)

Q64JEE Main 2021 · 25 JUL · SHIFT 1Medium

Law of Radioactive Decay

The half-life of ${}^{198}Au$ is 3 days. If atomic weight of ${}^{198}Au$ is 198 g/mol then the activity of 2 mg of ${}^{198}Au$ is [in disintegration/second]:

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Answer: (d)

$N = \frac{2\times10^{-3}}{198}\times6.02\times10^{23} \approx 6.08\times10^{18}$ .
$\lambda = \frac{0.693}{3\times86400\text{ s}} \approx 2.67\times10^{-6}\text{ s}^{-1}$ .
$A = \lambda N \approx 1.62\times10^{13} = 16.2\times10^{12}$ dis/s.
So the answer is (d) $16.18\times10^{12}$ .

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