A container is filled with a radioactive substance for which the half-life is` 2 days` . A week later, when the container is opened, it contains `5 g` of the substance. Approximately how many grams of the substance were initially placed in the container ?

Options

A. `40`
B. `60`
C. `80`
D. `100`

Answer

C

Explanation

For this substance` 7` days correspond to` 3.5` half-lives. Over `3` half-lives the sample reduces to `(1)/(2^(3))=(1)/(8)` of its initial mass.
After `4` half -lifes, the sample has only `(1)/(2^(4))=(1)/(16)` of its initial mass. Hence, after` 3.5` hlaf-lives the sample must contain somewhere between `1//8` and `1//6` of its initial mass.
Hence, 5g is somewhere between `1//8` and `1//16` of the initial mass .
So, the inital mass is somewhere between `8 xx 5=40 g` and `16 xx 5 =80 g`