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  • The activity of a sample reduces from to <img alt="\mathrm{\frac{A_{0}}{ \sqrt{2}}}" src=

The activity of a sample reduces from \mathrm{A_{0}} to \mathrm{\frac{A_{0}}{ \sqrt{2}}} in 2 hour. The activity after 6 hour more will be

Option: 1

\mathrm{\frac{A_0}{2 \sqrt{2}}}


Option: 2

\mathrm{\frac{A_0}{4}}


Option: 3

\mathrm{\frac{A_0}{4 \sqrt{2}}}


Option: 4

\mathrm{\frac{A_{0}}{8}}


Answers (1)

best_answer

\mathrm{\text{Activity is given by}\, A=\frac{A_0}{2^n}}.

\text { At } \mathrm{t}=2 \mathrm{hr} ; \mathrm{A}-\frac{\mathrm{A}_0}{\sqrt{2}}=\frac{\mathrm{A}_0}{2^\frac{\mathrm{t}}{\frac{t_1}{2}}}=\frac{\mathrm{A}_0}{2^{\frac{1}{2}}}
\mathrm{\Rightarrow t=\frac{t_{1 / 2}}{2} \Rightarrow t_{1 / 2}=4\, \mathrm{hrs}}

\mathrm{\text{Activity at\, t= 8 hrs }is}

\mathrm{A=\frac{A_0}{2^{t / t_{\frac{1}{2}}}}=\frac{A_0}{2^{8 / 4}}=\frac{A_0}{4}}.

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