The decay constant for a radioactive nuclide is 1.5 × 10 -5 s -1. Atomic weight of the substance is 60 g mole -1, ( NA = 6 × 10²³). The activity of 1.0 μ g of the substance is ___________ × 10 10 Bq. Numerical answer type. Work it out, then open the answer.

Answer: 15. Number of nuclei N = 10⁻⁶60 × 6 × 10²³ = 10¹⁶. Activity A = λ N = 1.5 × 10⁻⁵ × 10¹⁶ = 1.5 × 10¹¹ Bq. A = 15 × 10¹⁰ Bq, so the answer is 15.

The decay constant for a radioactive nuclide is 1.5 × 10 -5 s -1… | JEE Main 2023 (10 Apr, Shift 1)

Q34JEE Main 2023 · 10 APR · SHIFT 1Medium

Law of Radioactive Decay

The decay constant for a radioactive nuclide is 1.5 $\times$ 10 $-5$ s $-1$ . Atomic weight of the substance is 60 g mole $-1$ , ( $N_A = 6 \times 10^{23}$ ). The activity of 1.0 $\mu$ g of the substance is ___________ $\times$ 10 $10$ Bq.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

Number of nuclei $N = \frac{10^{-6}}{60} \times 6 \times 10^{23} = 10^{16}$ .
Activity $A = \lambda N = 1.5 \times 10^{-5} \times 10^{16} = 1.5 \times 10^{11}$ Bq.
$A = 15 \times 10^{10}$ Bq, so the answer is 15.

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