A radioactive sample at some instant has a disintegration rate of 5000 disintegrations per minute. After 5 minutes, the rate becomes 1250 disintegrations per minute. Then, the decay constant (per minute) is

Question

A radioactive sample at some instant has a disintegration rate of 5000 disintegrations per minute. After 5 minutes, the rate becomes 1250 disintegrations per minute. Then, the decay constant (per minute) is (A) 0.4ln2 (B) 0.2ln2 (C) 0.1ln2 (D) 0.8ln2

Tardigrade Admin · Accepted Answer

( A / A 0)=(1250/5000)=(1/4)=((1/2))( t / T ) ⇒ textT = ( textt/2) = ( text5/2) λ =( textln 2/ textT)=(2/5)l textn2 = text0.4ln2

Q. A radioactive sample at some instant has a disintegration rate of $5000$ disintegrations per minute. After $5$ minutes, the rate becomes $1250$ disintegrations per minute. Then, the decay constant (per minute) is

$0.4 l n 2$

$0.2 l n 2$

$0.1 l n 2$

$0.8 l n 2$

$\frac{A}{A _{0}} = \frac{1250}{5000} = \frac{1}{4} = (\frac{1}{2})^{\frac{t}{T}}$
$\Rightarrow T = \frac{t}{2} = \frac{5}{2}$
$λ = \frac{ln 2}{T} = \frac{2}{5} l n 2$
$= 0.4 l n 2$

Q. A radioactive sample at some instant has a disintegration rate of 5000 disintegrations per minute. After 5 minutes, the rate becomes 1250 disintegrations per minute. Then, the decay constant (per minute) is

0.4ln2

0.2ln2

0.1ln2

0.8ln2