Question

Suppose that you are given a 200 gram sample of a radioactive substance with a half-life of 45 days. How many grams will be left after 360 days?

Answer 1

Given:

The initial amount of the radioactive sample is,

`m=200\text{ g}`

The half-life is,

`t_{(1)/(2)}=45\text{ days}`

The total time span is,

`t=360\text{ days}`

To find:

How many grams will be left after 360 days?

Step-by-step explanation:

The number of half-life within the given time span is,

`\begin{gathered} n=\frac{t}{t_{(1)/(2)}} \\ n=(360)/(45) \\ n=8 \end{gathered}`

The sample left over after this time is,

`\begin{gathered} m^(\prime)=m*((1)/(2))^n \\ =200*((1)/(2))^8 \\ =200*(1)/(256) \\ =0.78\text{ g} \end{gathered}`

Hence, the leftover amount after the time is 0.78 g.