Question

A radioactive sample at any instant has its disintegration rate $5000 \, dpm$ . After $5 \, minutes$ , the rate is $1250 \, dpm$ . Then, the decay constant (per minute) is

• A. $0.8 \, ln2$
• B. $0.4 \, ln2$
• C. $0.2 \, ln2$
• D. $0.1 \, ln2$

Answer 1

Answer: (B)

$\frac{1250}{5000}=\frac{1}{2^{n}}$
$\left(n = 2\right)$
$T_{\frac{1}{2}}=\frac{t}{n}=\frac{5}{2}=2.5 \, min$
decay constant ,
$\lambda =\frac{l n 2}{T_{\frac{1}{2}}}=\frac{l n 2}{2.5}=0.4 \, ln2$