Question

Starting with a sample of pure ${ }^{66} Cu , 7 / 8$ of it decays into $Zn$ in $15 \,min$. The corresponding half-life is

• A. 10 min
• B. 15 min
• C. 5 min
• D. $7 \frac{1}{2}$ min

Answer 1

The Correct Option is C

$N = N_{0}\left(1-e^{-\lambda t}\right) $ $ \Rightarrow \frac{N_{0}-N}{N_{0}}=e^{-\lambda t} $ $\frac{1}{8} =e^{-\lambda t} $ $ \therefore 8 =e^{\lambda t} $ $ \Rightarrow 3 \ln 2 =\lambda t $ $\Rightarrow \lambda=\frac{3 \times 0.693}{15}$ Half-life period $t_{1 / 2} =\frac{0.693}{3 \times 0.693} \times 15 $ $t_{1 / 2} =5 \min$