Question

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year ______.

Options

• all the containers will have 5000 atoms of the material.

• all the containers will contain the same number of atoms of the material but that number will only be approximately 5000.

• the containers will in general have different numbers of the atoms of the material but their average will be close to 5000.

• none of the containers can have more than 5000 atoms.

Answer 1

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year the containers will in general have different numbers of the atoms of the material but their average will be close to 5000.

Explanation:

Half-life (T_1/2): Radioactivity is a process due in which a radioactive material spontaneously decays. The 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 `N = N_0/2`

Then t = T_1/2

Hence from `N = N_0e^(-λt)`

`N_0/2 = N_0e^(-λ(T_(1/2))`

⇒ `T_(1/2) = (log_e 2)/λ = 0.693/λ`

In half-life (t = 1 yr) of the material on average half, the number of atoms will decay. Therefore, the containers will in general have different numbers of atoms of the material, but their average will be approx 5000.