Question

The activity of a radioactive material is $6.4\times {10}^{–4}$ curie. Its half life is $5\text{days}$. The activity will become $5\times {10}^{–6}$ curie after

• A. $25\text{days}$
• B. $35\text{days}$
• C. $15\text{days}$
• D. $7\text{days}$

Answer 1

The correct option is B $35\text{days}$

Given data: Half life=$5\text{days}$

Activity after time $t$ is:
$A=\frac{A_0}{2^{\frac{t}{T_{1/2}}}}\Rightarrow 2^{t/5}=\frac{6.4\times {10}^{-4}}{5\times {10}^{-6}}=128=2^7\Rightarrow \frac{t}{5}=7\Rightarrow t=35\text{days}$
Thus the correct answer is $d$.