Question

A radioactive sample decays by $63$% of its initial value in $10s$. It would have decayed by $50$% of its initial value in

• A. $7s$
• B. $14s$
• C. $0.7s$
• D. $1.4s$

Answer 1

Answer: (A)

$7s$

Initial amount $=x$
After time $10s$
Amount $=37$
Number of half lives to get to $37$%
$N=\frac{log\left(\frac{x}{0.37x}\right)}{log\left(2\right)}=1.4344$ half lives.

$1.4344$ half lives $=10s$
$1$ half life $=6.97s$ (approximately $7$ seconds).
Hence, it would have decayed to $50$% in $7$ seconds.