Question

Starting with a sample of pure ${}_{66}Cu$, ${\left(\frac{7}{8}\right)}^{\text{th}}$ of it decays into $Zn$, in $15\text{min.}$ The corresponding half life is,

• A. $5\text{min}$
• B. $7\frac{1}{2}\text{min}$
  
• C. $10\text{min}$
• D. $14\text{min}$

Answer 1

The correct option is A $5\text{min}$

Here, ${\left(\frac{7}{8}\right)}^{\text{th}}$ of $N_0$ decayed in $15\text{min}$
$\Rightarrow \frac{1}{8}{N}_0$ remains after time $t$.

$\Rightarrow \frac{N}{N_0}=\frac{1}{8}$

Now, We know that,
$\frac{N}{N_0}=\frac{1}{2^n}$
Here, where $n$ is the number of half life periods elapsed.
So, $\frac{N}{N_0}=\frac{1}{8}=\frac{1}{2^n}\Rightarrow n=3$

Now,
$t=nT$
$15=3\times T$
$T=\frac{15}{3}=5\text{min.}$

Hence, $\left(A\right)$ is the correct answer.