Question

$7/8$th of a sample of ${}^{66}Cu$ decays into $Zn$ in $15min$. The corresponding half-life is

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

Answer 1

The correct option is C $5min$

We have the equation

$N_t=N_0(\frac{1}{2}{)}^{T/t}$

Where,

$T$ is the time period

$t$ is the half life

$N$ is the final amount

$N_0$ is the initial amount

It is given that the $7/8$th of a sample of ${}^{66}Cu$ decays into $Zn$ in $15$ minutes.

So,

$\frac{1}{8}N=N_0(\frac{1}{2}{)}^{15/t}$

then,

$\frac{1}{8}=(\frac{1}{2}{)}^{15/t}$

That is,

$\frac{15}{t}=3$

and

$t=5$ $min$

So half life is $5$ $minute.$