Half-life of radium is 1620 years. How many radium nuclei decay in 5 hours in 5 gm radium?
(Atomic weight of radium = 223)

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$1.72 \times 10^{20}$

$3.29 \times 10^{15}$

$9.1 \times 10^{12}$

$3.3 \times 10^{17}$

answer is B.

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Detailed Solution

$\begin{array}{l} N_{0} - N = N_{0} (1 - e^{- λ t}) \\ = (\frac{5}{223} \times 6.023 \times 10^{23}) (1 - e^{- \frac{\ln 2}{1620 \times 365 \times 24} \times 5}) \\ = 3.29 \times 10^{15} \end{array}$

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