Question 187: Atoms & Nuclei

Question

A radio active material is reduced to $$1 / 8$$ of its original amount in 3 days. If $$8 	imes 10^{-3} \mathrm{~kg}$$ of the material is left after 5 days the initial amount of the material is

Accepted Answer

The decay of a radioactive material follows an exponential decay law, which can be expressed as:
$$ N = N_0 \cdot \left(\frac{1}{2}ight)^{\frac{t}{T}} $$
where:
$$N$$ is the final amount of the material,
$$N_0$$ is the initial amount of the material,
$$t$$ is the elapsed time,
$$T$$ is the half-life of the material.
From the problem, we know that the material is reduced to $$1/8$$ of its original amount in 3 days. Therefore, the half-life of the material can be calculated as follows:
$$ \frac{1}{8} = \left(\frac{1}{2}ight)^{\frac{3}{T}} $$
This simplifies to $$2^{-3} = 2^{-\frac{3}{T}} $$, which gives $$ T = 1 \, 	ext{day} $$.
Knowing the half-life, we can now find the initial amount of the material. We know that after 5 days, $$8 	imes 10^{-3} \, 	ext{kg}$$ of the material is left. Therefore, we can write:
$$ 8 	imes 10^{-3} \, 	ext{kg} = N_0 \cdot \left(\frac{1}{2}ight)^{\frac{5}{1}} $$
Solving this equation for $$N_0$$ gives:
$$ N_0 = 8 	imes 10^{-3} \, 	ext{kg} \cdot 2^{5} = 256 	imes 10^{-3} \, 	ext{kg} = 0.256 \, 	ext{kg} = 256 \, 	ext{g} $$

Answer

64 g

Answer

256 g

Answer

32 g

Answer

40 g

Atoms & Nuclei

A radio active material is reduced to $1 / 8 of its original amount in 3 days. If 8 \times 10^{-3} \mathrm{~kg}$ of the material is left after 5 days the initial amount of the material is

Choose the correct answer: