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The half-life of a radioactive substance decaying by $dm/dt = -km$ (with $k > 0$) in terms of $k$ is:
A$\ln 2/k$
B$1/k$
C$k \ln 2$
D$2/k$
Answer & Solution
Correct answer: A. $\ln 2/k$
$m(t) = m_0 e^{-kt}$. Half-life: $m_0/2 = m_0 e^{-kt_{1/2}}$ ⇒ $kt_{1/2} = \ln 2$ ⇒ $t_{1/2} = \ln 2/k$.
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