Question

If a radioactive element has a half-life of 4 hours, then x grams of the element dwindles to x/2 grams after 4 hours. If a nuclear reactor has 800 grams of that radioactive element, find the amount of radioactive material after 16 hours.

Answer 1

50 grams

Explanation:

• The half life = 4 hours; original mass = x grams

• That means...
  in 4 hours the radioactive element will be reduced to x/2
  in 8 hours it will be reduced to 1/2 · x/2 = x/4
  in 12 hours --> 1/2 · x/4 = x/8
  in 16 hours -> 1/2 · x/8 = x/16

• We can determine a general equation for this:
  Mass remaining after n hours = x · (1/2)ⁿ
  where n = number of half-life periods = time/half life period

• Determine how many half-life period there are in 16 hours
  = 16/4 = 4. This will be our n

• The original mass of the element is 800 grams

• Therefore in 4 half-life periods it will reduce to 800 · (1/2)⁴
  = 800 · (1/16)
  = 50 grams ANSWER