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

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

Tardigrade Admin · Accepted Answer

(1250/5000)=(1/2n) (n = 2) T(1/2)=(t/n)=(5/2)=2.5 min decay constant , λ =(l n 2/T(1)2)=(l n 2/2.5)=0.4 ln2

Q. A radioactive sample at any instant has its disintegration rate $5000 d p m$ . After $5 min u t es$ , the rate is $1250 d p m$ . Then, the decay constant (per minute) is

$0.8 l n 2$

$0.4 l n 2$

$0.2 l n 2$

$0.1 l n 2$

$\frac{1250}{5000} = \frac{1}{2 ^{n}}$
$(n = 2)$
$T_{\frac{1}{2}} = \frac{t}{n} = \frac{5}{2} = 2.5 min$
decay constant ,
$λ = \frac{l n 2}{T _{\frac{1}{2}}} = \frac{l n 2}{2.5} = 0.4 l n 2$

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

0.8ln2

0.4ln2

0.2ln2

0.1ln2