Question

Question #e7a7d

Answer 1

Here's what I got.

Explanation:

For a given radioactive isotope, the nuclear half-life, `t_"1/2"`, tells you the time needed for 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.

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In your case, you know that the isotope has a half-life of `"120 s"`. If you start with an `"80-g"` sample, you will end up with

• `"80 g" * 1/2 = "80 g"/2^color(red)(1) ->` after `color(red)(1)` half-life passes
• `"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"`