Radioactive iodine-131 has a half-life of eight days. The amount of a 200.0 gram sample left after 32 days would be?

1 Answer

Answer:

#"12.5 g"#

Explanation:

Nuclear half-life, #t_"1/2"#, is the amount of time required for a quantity of a radioactive material to fall to half its value as measured at the beginning of the time period.

http://slideplayer.com/slide/6278114/#

In this question, the half-life of iodine-131 is #8# days, which means that after #8# days, half of the sample would have decayed and half would be left undecayed.

  • after #8# days (the first half-life):

#"200 g" /2 = "100 g"# decays and #"100 g"# are left.

  • after another ## days (two half-lives or #16# years):

#"100 g" /2 = "50 g"# decays and #"50 g"# are left.

  • after another #8# days (three half-lives or #24# years):

#"50 g" /2 = "25 g"# decays and #"25 g"# are left.

  • after another #8# days (four half-lives or #32# years):

#"25 g"/2 = "12.5 g"# decays and #"12.5 g"# are left.

So after four half-lives or #32# years, #"12.5 g"# of iodine-131 will be left.