Question

Amount of radioactive elements (activity) decrease with the passage of time as:
A. linearly
B. exponentially
C. parabolically
D. all of these

Answer 1

Hint: The law of radioactive decay states that the rate of the disintegration of the radioactive is directly proportional to the number of the nuclei of the radioactive elements which are present at that instant.

Complete step by step answer:
- The radioactive decay belongs to the first-order reaction because it depends on only one reactant species.
- As we know that the law of the radioactive decay gives us the relation between the rate of the disintegration of the radioactive and the number of nuclei present in the radioactive element i.e.
\[\text{N = }{{\text{N}}_{0}}{{\text{e}}^{-\lambda \text{t}}}\] or \[\text{N = }{{\text{N}}_{0}}\frac{1}{{{\text{e}}^{\lambda \text{t}}}}\]
- Here, N is the number of the nuclei present in the radioactive element at time = t, \[{{\text{N}}_{0}}\] is the number of the nuclei at the time = 0, \[\lambda \]is a constant which is known as decay constant and t is known as time.
- As we can see that the value of a number of the nuclei (N) gives the exponential relation in which the exponential term is inversely proportional to the time and decay constant.
- Now, as the radioactive process proceeds with time the amount of the radioactive element decreases.
 - So, we can say that the decrease in the amount occurs exponentially.
Therefore, option B is the correct answer.

Note: The half-life of a radioactive element is defined as the total time required to reduce the amount up to half of its initial value. The radioactive decay processes in which the unstable atom breaks down into smaller parts to become more stable.