A radioactive isotope having a half-life of 3 days was received after 12 days. It was found that there were 3 g of the isotope in the container. Find the initial weight of the isotope, when it was packed (antilog 1.203 = 16)

Question

A radioactive isotope having a half-life of 3 days was received after 12 days. It was found that there were 3 g of the isotope in the container. Find the initial weight of the isotope, when it was packed (antilog 1.203 = 16) (A) 12 g (B) 24 g (C) 36 g (D) 48 g

Tardigrade Admin · Accepted Answer

No. of half-lives, n=(12/3)=4 Amount left after n half-lives =(A0/2n) 3 g =(A0/24) or 3 g =(A0/16) ∴ A0=48 g

Q. A radioactive isotope having a half-life of $3$ days was received after $12$ days. It was found that there were $3 g$ of the isotope in the container. Find the initial weight of the isotope, when it was packed
(antilog $1.203 = 16$ )

$12 g$

$24 g$

$36 g$

$48 g$

No. of half-lives, $n = \frac{12}{3} = 4$

Amount left after $n$ half-lives $= \frac{A _{0}}{2 ^{n}}$

$3 g = \frac{A _{0}}{2 ^{4}}$

or $3 g = \frac{A ^{0}}{16}$

$∴ A^{0} = 48 g$

Q. A radioactive isotope having a half-life of 3 days was received after 12 days. It was found that there were 3g of the isotope in the container. Find the initial weight of the isotope, when it was packed (antilog 1.203=16)

12g

24g

36g

48g