Question

Half life of a radio active element is $5$min $10$sec. Time taken for $90$% of it to disintegrate is nearly

• A. $100min$
• B. $1000sec$
• C. $10$${}^{4}sec$
• D. ${10}^{4}min$

Answer 1

Answer: (A), (B)

$100min$
$1000sec$

Half life of the material is $=(5\times 60+10)seconds$
$=310seconds$

From integrated rate law:

$\lambda =\frac{2.303}{t}ln\left(\frac{N_0}{N}\right)$ and also $\lambda =\frac{0.693}{t_{1}2}$

$\Rightarrow \frac{0.693}{310}=\frac{2.303}{t}ln\left(\frac{100}{10}\right)$

$\Rightarrow t=1030seconds\approx 1000seconds$