Question

What is the half-life of a radioactive substance if $87.5\%$ of any given amount of the substance disintegrate in $40$ minutes?

• A. $160$ min
• B. $10$ min
• C. $20$ min
• D. $13$ min

Answer 1

Answer: (D)

$13$ min

Radioactive reacting have order one so

$Kt=2.303log\frac{[R{]}_0}{[R{]}_t}$

$K\times 40=2.303log\frac{[R{]}_0}{12.5[R{]}_0}\times 100$

$K=0.052mi{n}^{-1}$

$t_{50\%}=\frac{0.693}{K}$

$t_{50\%}=\frac{0.693}{0.052}$

$t_{50\%}=13.32min$