Question

The half-life of ${}^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of ${}^{215}At$ to decay to $1/{16}^{th}$ of its initial value is

• A. $400\mu s$
• B. $6.3\mu s$
• C. $40\mu s$
• D. $300\mu s$

Answer 1

The correct option is A $400\mu s$

Since $\frac{1}{16}=\frac{1}{2^4}$, it follows that the time taken for the radioactivity to decay to $\frac{1}{16}th$ of its initial value $=$ four times the half-life of the sample $=4t_{1/2}=4\times 100\mu s=400\mu s$.