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 48.4 mg 99Mo remaining? Report your answer rounded to the tenth of a gram. Do not include units.

Answer 1

Half life of molybdenum (t_1/2) = 66 hours.

then, radioactive decay constant () = 0.693/t_1/2 = 0.693/66 = 0.0105 hour^-1.

now, radioactive decay equation is.

ln ( N₀/N) = t ( 1)

where, No = initial molecules of the Mo⁹⁹

N = molecules of Mo ⁹⁹ after time t

= ( 48.4*10^-3*6*023*10²³)/99

t = time interval = 22 days = 22*24 hours.

= 0.0105 hour^-1

now putting the above value in Eq. 1.

ln ( N / 48.4*10^-3*6.023*10²³ 99) = 0.0105 *22*24

or, N*99*10^-20/48.4*6.023 = e^5.544

or, N*99*10^-20/48.4*6.023 = 230.44

or, N = (230.44*48.4*6.023*10²⁰/99)

or, N = 678.5*10²⁰

hence, moles of Mo⁹⁹ was present = 678*10²⁰/6.023*10²³

or,

grams of Mo = (678*10²⁰*99/6.023*10²³ )

= 11153*10^-3  = 11.12 ( upto tenth of a gram)