Question #e7a7d

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"#