Question

The half-life of a radioactive element is $100$ minutes. The time interval between the stages to $50\%$ and $87.5\%$ decay will be:

• A. $100min$
• B. $50min$
• C. $200min$
• D. $25min$

Answer 1

The correct option is C $200min$

$k=\frac{0.693}{t_{1/2}}$

$k=6.93\times {10}^{-3}{min}^{-1}$

$t=\frac{2.303}{k}log\frac{100}{12.5}-\frac{2.303}{k}log\frac{100}{50}$

$t=\frac{2.303}{6.93\times {10}^{-3}}\times 0.6020$

$t=200min$