Question

$DDT$ on exposure to water decomposes. It's half-life $=$ $10$ years. How much time it will take for its decomposition to $99$% ?

• A. $50$ years
• B. $66.5$ years
• C. $500$ years
• D. $700$ years

Answer 1

Answer: (B)

$66.5$ years

$k=\frac{0.693}{10}y{r}^{-1}$

when $t$ is $99$%
$=\frac{2.303}{t}\log \frac{a}{a-0.99a}=\frac{2.303}{t}\log {10}^2$
$\frac{0.693}{10}=\frac{2.303}{t_{99}}\times 2$

or

$t=\frac{10}{0.693}\times 2.303\times 2=66.5$years

Option B is correct.