Question

If N₀ active nuclei become $\frac{N_o}{16}$ in 80 days. Find the half-life of nuclei?

• A. 40 days
• B. 20 days
• C. 60 days
• D. 30 days

Answer 1

The correct option is B

20 days

Step 1: Use the radioactive formula

The activity of radioactive substance at any time t is given by

$\therefore N=N_0{e}^{-\lambda t}$

Given that $\frac{N}{N_0}=\frac{1}{16}\text{at time}t=80\text{days}$
$\begin{array}{l}\frac{1}{16}=e^{-80\lambda }\\ e^{40\lambda }=16\\ \lambda =\frac{1\text{n}\left(16\right)}{80}\end{array}$

We know that:

$t_{\frac{1}{2}}=\frac{\text{ln}\left(2\right)}{\lambda }$

Step 2: After putting the value of $\lambda$ in the above equation

$\begin{array}{l}{t}_{\frac{1}{2}}=\frac{\text{ln}\left(2\right)}{\text{ln}\left(16\right)}\times 80\\ t_{\frac{1}{2}}=20\text{days}\end{array}$

Final Answer: Hence, the correct answer is option (B).