A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope ?

Question

A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope ? (A) 12 g (B) 36 g (C) 48 g (D) 24 g

Tardigrade Admin · Accepted Answer

Given tm = 3 Total time T= 12 No. of half lives (n)=(12/3)=4 ((1/2))n =(N/N0) ∴ ((1/2))4 =(3/N0) (3/N0) =(1/16) N0 =48 g

Q. A radioactive isotope having a half - life period of $3$ days was received after $12$ days. If $3 g$ of the isotope is left in the container, what would be the initial mass of the isotope ?

$12 g$

$36 g$

$48 g$

$24 g$

Given $t m = 3$
Total time $T = 12$
No. of half lives (n)= $\frac{12}{3} = 4$
$(\frac{1}{2})^{n} = \frac{N}{N _{0}}$
$∴ (\frac{1}{2})^{4} = \frac{3}{N _{0}}$
$\frac{3}{N _{0}} = \frac{1}{16}$
$N_{0} = 48 g$

Q. A radioactive isotope having a half - life period of 3 days was received after 12 days. If 3g of the isotope is left in the container, what would be the initial mass of the isotope ?

12g

36g

48g

24g