Question

The half life of a radioactive element is $10$ hours. The fraction of initial radioactivity of the element that will remain after $40$ hours is:

• A. $\frac{1}{2}$
• B. $\frac{1}{16}$
• C. $\frac{1}{8}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{1}{16}$

If half life is 10 hours,
$\lambda =\frac{ln2}{10h}$

$⟹C=C_0{e}^{-\lambda t}$$=C_0{e}^{-\frac{ln2}{10h}40h}$

$⟹\frac{C}{C_0}=\frac{1}{16}$