Question

10grams of a radioactive element is disintegrated to 1gram in 2.303minutes. The half-life (in minutes) of that radioactive element is:

• A. $\frac{1}{0.693}$
• B. $6.93$
• C. $1$
• D. $0.693$

Answer 1

The correct option is D $0.693$

Using integrate reaction rate:
$N=N_0{e}^{-\lambda t},t=2.303=ln10$
$1=10e^{-\lambda t}$
$\Rightarrow \frac{1}{10}=e^{-\lambda ln10}$
$\Rightarrow ln10=\lambda ln10$

$\Rightarrow \lambda =1$

So, half life of the material $=\frac{0.693}{\lambda }=0.693mi{n}^{}$