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If the half life for the radioactive decay of zirconium 84 is 26 minutes and i start with a 175 gram sample, how much will be left over after 104 minutes? show work or explain your answer.

Respuesta :

superman1987

Answer:

10.94 g.

Explanation:

  • The decay of zirconium 84 is a first order reaction.
  • The rate constant of the reaction (k) in a first order reaction = ln (2)/half-life = 0.693/(26.0 min) = 0.02665 minā»Ā¹.
  • The integration law of a first order reaction is:

kt = ln [Aā‚€]/[A]

k is the rate constant = 0.02665 minā»Ā¹.

t is the time = 104.0 min.

[Aā‚€] is the initial percentage of radioisotope = 175.0 g.

[A] is the remaining percentage of radioisotope = ??? g.

āˆµ kt = ln [Ao]/[A]

āˆ“ (0.02665 minā»Ā¹)(104.0 min) = ln (175.0 g)/[A]

2.772 = ln (175.0 g)/[A]

  • Taking exponential to both sides:

15.99 = (175.0 g)/[A]

āˆ“ [A] = (175.0 g)/(15.99) = 10.94 g.

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