Question

For a radioactive material, number of nuclei decreases by $10\%$ in $20$ minutes. Find percentage of decayed nuclei in $1$ hour.

• A. $30\%$
• B. $17.5\%$
• C. $27\%$
• D. $73\%$

Answer 1

The correct option is D $73\%$

In $20$ minutes $\to$ $90\%$ of initial number of nuclei $\Rightarrow 90\%\left(N_0\right)=0.9N_0$
In $40$ minutes $\to$ $90\%$ of $\left(0.9N_0\right)=0.81N_0$
In $1$ hour $\to$ $90\%$ of $\left(0.81N_0\right)=0.729N_0$
$=0.73N_0\simeq 73\%$