Question #188b6

1 Answer
Aug 8, 2017

Answer:

#"23 g"#

Explanation:

All you have to do here is to use the following equation

#A_t = A_0 * (1/2)^color(red)(n)#

Here

  • #A_t# is the mass of the substance that remains undecayed after a period of time #t#
  • #A_0# is the initial mass of the substance
  • #color(red)(n)# represents the number of half-lives that pass in a given time period #t#

In your case, you know that the initial mass of the substance is equal to #"35 g"#.

Now, the number of half-lives that pass in a given time period #t# can be calculated by dividing the period of time by the half-life of the substance, #t_"1/2"#.

#color(red)(n) = t/t_"1/2"#

In your case, the number of half-lives that pass in #2100# years is equal to

#color(red)(n) = (2100 color(red)(cancel(color(black)("years"))))/(3400color(red)(cancel(color(black)("years")))) = 0.617647#

Plug this into the aforementioned equation and solve for #A_"2100 years"#, the mass of the substance that remains undecayed after #2100# years

#A_ "2100 years" = "35 g" * (1/2)^0.617647 = color(darkgreen)(ul(color(black)("23 g")))#

The answer is rounded to two **[sig figs](