Question

Five technetium-99m generators in the Nuclear Medicine Lab which used to be located on Level 10 of Building 14 of the City campus of the Royal Melbourne Institute of Technology (RMIT) in Melbourne, Victoria, Australia. Image Credit: By Kieran Maher. [Public domain], from Wikimedia Commons. In the previous question, the technetium-99 generator was shown unshielded. When the apparatus containing molybdenum-99 is distributed to hospitals, it is enclosed in a lead-lined box. The half-life of molybdenum-99 is 66 hours. The generators need to be returned to the supplier for recharging about every two weeks. How many grams of the 99Mo were originally installed in the box, if after 22 days there were 43.5 mg 99Mo remaining? Report your answer rounded to the tenth of a gram. Do not include units.

Answer 1

grams of the ⁹⁹Mo originally installed in the box = 11.1 g              (exact amount is 11.136 g)

Explanation

Time elapsed = 22 days = 22 days * (24 hours/day) = 528 hours

number of half lives passes, X = (time elapsed) / (half life)

X = (528 hours) / (66 hours)

X = 8

According to decay law,

final amount = initial amount / 2^X

final amount = 43.5 mg = 43.5 x 10^-3 g

43.5 x 10^-3 g = initial amount / 2⁸

initial amount = (43.5 x 10^-3 g) * 2⁸

initial amount = (43.5 x 10^-3 g) * 256

initial amount = 11.136 g