Question

The half-life of a radioactive element is 10 minutes. Find the time in which its activity reduces to 1/16 of the original.

Hint:

When quantity becomes \( \frac{1}{2^n} \), the number of half-lives is \( n \). Multiply by given half-life time to find the total elapsed time.

Answer 1

Use the formula: \[ N = N_0 \cdot \left(\frac{1}{2}\right)^n \Rightarrow \frac{N}{N_0} = \frac{1}{16} = \left(\frac{1}{2}\right)^4 \Rightarrow n = 4 \text{ half-lives} \] \[ \text{Time } t = n \cdot T_{1/2} = 4 \cdot 10 = 40\,\text{minutes} \] Final Answer: \[ \boxed{40\,\text{minutes}} \]