For a radioactive sample, the initial activity of the material was 8 cps and after 3 h it becomes 1 cps . The half-life of the sample is

Question

For a radioactive sample, the initial activity of the material was 8 cps and after 3 h it becomes 1 cps . The half-life of the sample is (A) 2h (B) 1 h (C) 3h (D) 4h

Tardigrade Admin · Accepted Answer

Here A0 = 8 counts, A= 1 count and t=3 h . (A/A0)=((1/2))n â (1/8)=((1/2))n or ((1/2))3=((1/2))n⇒ n=3 So, T1 / 2 = (t/n) = (3/3)= 1 h

Q. For a radioactive sample, the initial activity of the material was $8$ $c p s$ and after $3 h$ it becomes $1$ $c p s$ . The half-life of the sample is

$2 h$

$1 h$

$3 h$

$4 h$

Here $A_{0} = 8$ counts, $A =$ $1$ count and $t = 3 h$ .
$\frac{A}{A _{0}} = (\frac{1}{2})^{n}$
$\Rightarrow \frac{1}{8} = (\frac{1}{2})^{n}$
or $(\frac{1}{2})^{3} = (\frac{1}{2})^{n} \Rightarrow n = 3$
So, $T_{1/2} = \frac{t}{n} = \frac{3}{3} = 1 h$

Q. For a radioactive sample, the initial activity of the material was 8 cps and after 3h it becomes 1 cps . The half-life of the sample is

2h

1h

3h

4h