Question

A radioactive substance has an average life of 5 hours. In a time of 5 hours
 A. Half of the active nuclei decay
 B. Less than half of the active nuclei decay
C. More than half of the active nuclei decay
D. All active nuclei decay

Answer 1

Hint: A radioactive substance is a substance that is highly unstable and loses energy by the process of disintegration. The substance taken a time to reduce to half of its initial amount is half-life of the substance. The rate of disintegration of radioactive substances is directly proportional to the amount of substance occurring.


Complete answer:
In a radioactive element all the nuclei do not decay simultaneously. But the nature of the disintegration process is statistical. That is, it cannot be stated continuously in which nucleus will decay when the time of disintegration of a nucleus between 0 and infinity. The mean lifetime of all nuclei of a radioactive element is called mean life of a radioactive element.

If 𝞴 is the disintegration constant of a radioactive substance and then average life =1
And also half-life = 0.693
                                =0.693 × average life
In a single average life is more than 63% of radioactive decay.
Hence, the correct answer is option C


Note: There is no need to confuse the half-life and average life of a radioactive substance. Half-life, in radioactivity, is the amount of time needed for half of a radioactive sample's atomic nuclei to decay (change spontaneously into other nuclear species by emitting particles and energy) and The half-life of the material divided by the natural log 2 yields a value of 0.693, which is the average life of any radioactive isotope.