- The containers will in general have different numbers of the atoms of the material but their average will be close to 5000.
Solution:
Key concept:
Half life ( T1/2): Radioactivity is a process due to which a radioactive material spontaneously decays. Time interval in which the mass of a radioactive substance or the number of its atom reduces to half of its initial value is called the half life of the substance.
i.e., if $\text{N}=\frac{\text{N}_0}{2}$
Then $\text{t}=\text{T}_\frac{1}{2}$
Hence from $\text{N}=\text{N}_0\text{e}^{-\lambda\text{t}}$
$\frac{\text{N}_0}{2}=\text{N}_0\text{e}^{-\lambda\Big(\text{T}_\frac{1}{2}\Big)}\Rightarrow\ \text{T}_\frac{1}{2}=\frac{\log_\text{e}2}{\lambda}=\frac{0.693}{\lambda}$
In half-life (t = 1yr) of the material on the average half the number of atoms will decay. Therefore, the containers will in general have different number of atoms of the material, but their average will be approx 5000.