Question 468: Atoms & Nuclei

Question

A sample of radioactive element contains $$8 	imes 10^{16}$$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

Accepted Answer

Half life, $$T=15$$ days, time $$t=60$$ days $$=4 T$$
The number of nuclei remaining is given by
$$\begin{aligned}
& \mathrm{N}=\mathrm{N}_0\left(\frac{1}{2}ight)^{\mathrm{n}} \quad =\mathrm{N}_0\left(\frac{1}{2}ight)^4 \quad \mathrm{n}=	ext { no. of half-lives } \
& =\frac{1}{16} \mathrm{~N}_0 \quad=\frac{1}{16} 	imes 8 	imes 10^{16} \
& =0.5 	imes 10^{16} \
& 	herefore 	ext { No. of nuclei decayed }=\mathrm{N}_0-\mathrm{N} \
& =8 	imes 10^{16}-0.5 	imes 10^{16}=7.5 	imes 10^{16} \
\end{aligned}$$

Answer

$$7.5 	imes 10^{16}$$

Answer

$$2.0 	imes 10^{16}$$

Answer

$$0.5 	imes 10^{16}$$

Answer

$$4.0 	imes 10^{16}$$

Atoms & Nuclei

A sample of radioactive element contains $8 \times 10^{16}$ active nuclei. The halt-life of the element is 15 days. The number of nuclei decayed after 60 days is

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