Question 2: Atoms & Nuclei

Question

If half life of an element is $$69.3 \mathrm{~h}$$, then how much of its percent will decay in 10th to 11th $$\mathrm{h}$$. Initial activity $$=50 ~\mu \mathrm{~Ci}$$

Accepted Answer

Given, half life of an element, $$t_{1 / 2}=69.3 \mathrm{~h}$$
Let initial amount (at $$t=0$$) of radioactive element $$\left(t_{1 / 2}ight)=69.3 \mathrm{~h}$$
Active nuclei at $$t=10 \mathrm{~h}$$,
$$N_1=N_0 e^{-10 \lambda}$$
Active nuclei at $$t=11 \mathrm{~h}, N_2=N_0 e^{-11 \lambda}$$
% decay in 10th to 11th $$\mathrm{h}$$
$$\begin{aligned}
& =\frac{N_1-N_2}{N_1} 	imes 100=\frac{N_0 e^{-10 \lambda}-N_0 e^{-11 \lambda}}{N_0 e^{-10 \lambda}} 	imes 100 \
& =\left(1-e^{-\lambda}ight) 	imes 100 \
& \begin{aligned}
& =\left[1-e^{\frac{-0.693}{69.3}}ight] 	imes 100 \quad\left[\because 	ext { where, } \lambda=\frac{0.693}{t_{1 / 2}}ight] \
& =\left[1-e^{-0.01}ight] 	imes 100=[1-0.99] 	imes 100 \
& =0.01 	imes 100=1 \%
\end{aligned}
\end{aligned}$$

Answer

1%

Answer

2%

Answer

3%

Answer

4%

Atoms & Nuclei

If half life of an element is $69.3 \mathrm{~h}, then how much of its percent will decay in 10th to 11th \mathrm{h}. Initial activity =50 ~\mu \mathrm{~Ci}

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