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Use the References to access important values if needed for this question. Radioactive decay can be described by the following equation where is the original amount of the substance, is the amount of the substance remaining after time , and is a constant that is characteristic of the substance. For the radioactive isotope iron-55, is . If the original amount of iron-55 in a sample is 74.0 mg, how much time is needed for the amount of iron-55 that remains to fall to 32.7 mg? years

Respuesta :

Answer:

Explanation:

  • from the Radioactive decay equation ; lnA = ln Ao - kt
  • Ao = original amount of substance = 74mg
  • where A = is the amount of the substance remaining after time t = 32.7mg,
  • k = is a constant that is characteristic of the substance = 2.67 x 10^-1 years^-1
  • t = ?

All radioactive substances follow the first order kinetics, as such the rate constant for first order is given as , k = 1/t ln[Ao/A]

  • hence t = 1/k ln[Ao/A]
  • plugging the values in the equation;
  • t = 1/0.267 x ln [74/32.7]
  • t = 3.745 ln(2.2629)
  • t = 3.05years is the time needed