Question

Starting with a sample of pure ${}^{66}Cu,7/8$ of its 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 B $15min$

Let initial amount of Cu be N.

Fraction decayed in 1st half life = $\frac{1}{2}$N

Fraction decayed in 2nd half lives = $\frac{1}{4}$N

Fraction decayed in 3 half lives = $\frac{1}{8}$N

Total amount decayed in 3 half lives = $\frac{1}{2}$N + $\frac{1}{4}$N + $\frac{1}{8}$N = $\frac{7}{8}$N

$\therefore$ 3 half lives = 15 minutes

$\therefore$ Half life of the Cu is 5 minutes.