# Question #e7a7d

##### 1 Answer

Here's what I got.

#### Explanation:

For a given radioactive isotope, the **nuclear half-life**, **half** of an initial sample of this isotope to undergo radioactive decay.

This means that **with every** half-life that passes, the mass of the sample will be **halved**.

In your case, you know that the isotope has a half-life of

#"80 g" * 1/2 = "80 g"/2^color(red)(1) -> # after#color(red)(1)# half-lifepasses#"80 g"/2^color(red)(1) * 1/2 = "80 g"/2^color(red)(2) -># after#color(red)(2)# half-lives pass#"80 g"/2^color(red)(2) * 1/2 = "80 g"/2^color(red)(3) -># after#color(red)(3)# half-lives pass

#vdots#

and so on. You can thus say that your sample will contain

#"After 120 s"#

#(120 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(1) implies "80 g"/2^color(red)(1) = "40 g"#

#"After 240 s"#

#(240 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(2) implies "80 g"/2^color(red)(2) = "20 g"#

#"After 480 s"#

# (480 color(red)(cancel(color(black)("s"))))/(120 color(red)(cancel(color(black)("s")))) = color(red)(3) implies "80 g"/2^color(red)(3) = "10 g"#