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

Answer 1

Answer: (C)

$ \, N \, = \, N_{0}\left(\right.1- \, e^{- \lambda t}\left.\right)$ , N - The amount of substance decayed.
$\Rightarrow \, \, \frac{N_{0} - N}{N_{0}}=e^{- \lambda t}$
$\therefore \, \frac{1}{8}=e^{- \lambda t}$
$\Rightarrow \, 8=e^{\lambda t}$
$\Rightarrow $ $3ln2 \, =\lambda t$
$\Rightarrow \, \, \, \lambda =\frac{3 \, \times \, 0 .693}{15}$
Half-life period
$\lambda =5min$