Question

In one average life

• A. Half the active nuclei decay
• B. Less than half the active nuclei decay
• C. More than half the active nuclei decay
• D. All the nuclei decay

Answer 1

The correct option is C More than half the active nuclei decay

Let's take a sample of a radioactive element with $N_0$ nuclide. Average time $t_{avg}$= $1/\lambda$
Let's see how many nuclei remain after $t_{avg}$ N =$N_0{e}^{-}\lambda t$
Substituting value of t we get
N =$N_0{e}^{-\lambda \frac{1}{\lambda }}$
N = $N_0/e$
So after one average-life $N_0/e$ nuclei would remain acitive.
That means $N_0-\left(N_0/e\right)$ Would have decayed wheras in a half-life only $N_0/2$ would have decayed.
So in one average life more than half the active nuclei decay.