Question

87.5% of a radioactive substance disintegrates in 40 minutes. What is the half life of the substance

• A. 13.58 min
• B. 135.8 min
• C. 1358 min
• D. None of these

Answer 1

Answer: (A)

13.58 min

Answer 2

Determination of k by substituting the respective values.

$k = \frac{2.303}{t}\log\frac{a}{a - x} = \frac{2.303}{40}\log\frac{a}{a - 0.875a}$ $= \frac{2.303}{40}\log\frac{a}{0.125a}$ $= \frac{2.303}{40}\log 8$ $= 0.051\mspace{6mu}\min^{- 1}{}$

$\therefore$ $t_{1/2} = \frac{0.693}{k} = \frac{0.693}{0.051} = 13.58\mspace{6mu}\min$