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  • An experiment is performed to determine the half- life of a radioactive substance which emits one beta particle for each decay process. Observations show that an average of 8.4 <img alt="\beta" src

An experiment is performed to determine the half- life of a radioactive substance which emits one beta particle for each decay process. Observations show that an average of 8.4 \beta-particles are emitted each second by 2.5 mg of the substance. The atomic weight of the substance is 230. Calculate the half- life of the substance.

Option: 1

\mathrm{1.71 \times 10^{10} \text { year }}


Option: 2

1.76 \times 10^{10} \text { year }


Option: 3

1.81 \times 10^{10} \text { year }


Option: 4

1.91 \times 10^{10} \text { year }


Answers (1)

best_answer

\mathrm{\text { Given that activity }=8.4 \mathrm{sec}^{-1}}

According to Avogadro’s hypothesis, the number of atoms in 2.5 mg

\mathrm{N=\frac{6.02 \times 10^{23}}{230} \times 2.5 \times 10^{-3}=6.54 \times 10^{18}}

\mathrm{\text { Now } \lambda \mathrm{N}=8.4 \mathrm{sec}^{-1}}

\mathrm{\begin{aligned} & \therefore \lambda=\frac{8.4}{N}=\frac{8.4}{6.54 \times 10^{18}}=1.28 \times 10^{-18} \mathrm{sec}^{-1} \\ & \therefore \mathrm{T}=\frac{0.6931}{\lambda}=\frac{0.6931}{1.28 \times 10^{-18}} \text { sec. }=1.71 \times 10^{10} \text { year } \end{aligned}}

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