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  • Half life of radium is 1620 year. How many radium nuclei decay in 5 hour in radium. (Atomic weight of radium <

Half life of radium is 1620 year. How many radium nuclei decay in 5 hour in 5 \, \mathrm{gm} radium. (Atomic weight of radium = 223).

Option: 1

9.1 \times 10^{12}


Option: 2

3.23 \times 10^{15}


Option: 3

1.72 \times 10^{20}


Option: 4

3.3 \times 10^{17}


Answers (1)

best_answer

\mathrm{\text{Number of nuclei initially}=\frac{5}{223} \times 6.02 \times 10^{23}}
\mathrm{\Rightarrow N_0=13.5 \times 10^{21} }

\mathrm{t_{1 / 2}=1620 \times 365 \times 29 \, \mathrm{hrs} }
        \mathrm{=1.41 \times 10^7 \mathrm{hrs}}.

\mathrm{N=\frac{N_0}{t^{t / t_1 / 2}}=\frac{N_0}{2^{5 / 1.41 \times 10^7}}}

Number of nuclei decayed
\mathrm{=N_0-N=N_0-\frac{N_0}{2^{5 / 1.41 \times 10^7}} }
\mathrm{=3.15 \times 10^{15} }

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Gaurav

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