Respuesta :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf C. \ 2.5 \ grams }}[/tex]

Explanation:

We are asked to find how much of a 40 gram sample remains after 12 years.

Iron-55 has a half-life of 3 years. Therefore, after 12 years, 4 half-lives have been completed.

  • 12 years/3 years = 4 half-lives

Every time a half-life is completed, half of the sample's mass decays. Remember we start with a 40 gram sample.

  • 1 half- life: 40 g / 2 = 20 g
  • 2 half-lives: 20 g / 2= 10 g
  • 3 half-lives: 10 g / 2 = 5 g
  • 4 half-lives: 5 g / 2 = 2.5 g

There is also a formula that can be used to solve this problem.

[tex]A= A_o(\frac {1}{2})^{\frac{t}{hl}[/tex]

Where A₀ is the initial amount, t is the time, and hl is the half-life.

We know 40 grams is the inital amount, 12 years is the time, and 3 years is the halflife.

  • A₀= 40 g
  • t= 12
  • hl= 3

[tex]A= 40 \ g (\frac{1}{2})^\frac{12}{3}[/tex]

[tex]A= 40 \ g (\frac{1}{2})^4[/tex]

[tex]A= 40 \ g * 0.0625[/tex]

[tex]\bold {A= 2.5 \ g}[/tex]

After 12 years, 2.5 grams of Iron-55 will remain.

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