Question

In one average life:
A. Half the radioactive nuclei decay
B. Less than half the radioactive nuclei decay
C. More than half the radioactive nuclei decay
D. All the nuclei decay

Answer 1

Hint: The average life of radioactive nuclei can be defined as the reciprocal of the decay constant. Understand the above definition of the average life of the radioactive nuclei and find out the correct answer from the above given options.

Complete step by step answer:
The average life is the expected life for the radioactive substance within a sample. This average life of the radioactive substance is denoted by the Greek letter $$\tau$$
The average life can be found or calculated for a radioactive substance by using the decay constant.
The average life of a radioactive substance is equal to the reciprocal of the decay constant. The decay constant of a radioactive substance is denoted by the Greek letter lambda $$\lambda$$
Average life of the radioactive substance is the amount of time required for it to decay by 63.2% of its original amount which is more than half the nuclei decay.

Since the average life is more than half the nuclei decay, from the above given options the correct answer is option (C).


Note: The average life of a radioactive substance is different from the half life of it. The half life of a radioactive substance can be defined as the time required for half of the radioactive substance to decay which is mathematically represented as follows:
$$t_{1/2}={\displaystyle \frac{\ln (2)}{\lambda }}$$ Whereas the average of the radioactive substance is $$\tau ={\displaystyle \frac{\mathrm{l}}{\lambda }}$$
Hence both average life and half life of a radioactive substance are different.