Question

Consider a radioactive material of half-life 1.0 minute. If one of the nuclei decays now, the next one will decay
A) After 1 minute
B) After $\dfrac{1}{{{{\log }_e}2}}$ minute
C) After 1/N minute, where N is the number of nuclei present at that moment
D) After any time

Answer 1

Hint:This is a theoretical question from radioactivity. If we know the basic idea of what radioactivity is and how elements decay, then we can easily solve this problem.


Complete answer:
In order to change into a more stable state, a radioactive atom will naturally produce radiation in the form of energy or particles. This process is called radioactive decay. During radioactive decay, an element transforms into another one on its own. Alpha decay, beta decay, and gamma decay are three of the decay types that all involve the emission of one or more particles.
Radioactive elements decay or dissolve into nontoxic substances. While certain isotopes disintegrate in hours or even minutes, others do so very slowly.
At the atomic level, radioactive decay is a random process. No matter how long an atom has existed, quantum theory says it is impossible to predict when an atom will decay. Radioactive decay is completely unpredictable. You could never know in advance how an atom will decay if you were to take only one.

Hence, the correct option is Option (D).


Note:The law of radioactive decay states, “If a radioactive sample contains N nuclei, at a given instant the ratio of the radioactive decay ($ - \dfrac{{dN}}{{dt}}$) to the number of nuclei present at that instant is a constant.”