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  • Find the amount of mercury deft after a time period of 300 hour if stable mercury is obtained by <img alt="\mathrm{ \hat{\beta}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm

Find the amount of mercury deft after a time period of 300 hour if stable mercury is obtained by \mathrm{ \hat{\beta}} emission of 2 g of \mathrm{ { }_{79} \mathrm{Au}^{198}} whose \mathrm{t_{1 / 2}}  is 65 \mathrm{~h}.

Option: 1

1.3758 g


Option: 2

1.9103 g


Option: 3

1.9982 g


Option: 4

0.7586 g


Answers (1)

best_answer

\mathrm{\begin{aligned} & { }_{79} \mathrm{Au}^{198} \stackrel{-\beta}{\longrightarrow}{ }_{80} \mathrm{Hg}^{198} \\ & K=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{65} \end{aligned}}

\mathrm{\text { After } 300 \mathrm{~h}, k=\frac{2.303}{300} \log \frac{a}{a-x}}

\mathrm{\begin{gathered} \frac{0.693}{65}=\frac{2.303}{300} \log \frac{2}{2-x} \\ 24.48=\frac{2}{2-x} \\ 12.21(2-x)=1 \\ x=1.91 \end{gathered}}

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Ritika Jonwal

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