Question 475: Atoms & Nuclei

Question

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

Accepted Answer

Given:
Total time, $$\mathrm{T}=10$$ years
Half life, $$\mathrm{T}_{1 / 2}=5$$ years
$$	herefore \quad$$ No. of half lives, $$\mathrm{n}=\frac{10}{5}=2$$
From $$\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}ight)^{\mathrm{n}}$$
$$	herefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}ight)^2=\frac{1}{4}$$
$$	herefore \quad$$ After 10 years, $$\frac{1}{4}^{	ext {th }}$$ of the original substance will remain.
$$\Rightarrow\left(1-\frac{1}{4}ight)=\frac{3}{4} 	imes 100=75 \%$$ of the fraction would get decayed.

Answer

25%

Answer

50%

Answer

75%

Answer

100%

Atoms & Nuclei

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

Choose the correct answer: