In the previous question, the technetium-99 generator was shown unshielded. When

Question

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

Explanation / Answer

Answer:

For nuclear decay,

N=N0(0.5)^(t/t1/2)

Where N=Amount of compound at time t, t1/2=half life, N0=initial amount of compound.

Given N0=?, N=22.8 mg at t=22 days t=66 hrs=2.75 days. (Since 1 day=24 hr)

Therefore (22.8 mg)=N0 (0.5)^[22 days/2.75 days]

N0=(22.8 mg)/(0.5)^8=5836.8 mg =5.837 g ~ 5.8 g. (Since 1 g=1000 mg)

Therefore original mass of 99Mo in the box = 5.8

Please let me know if you have any doubt. Thanks.

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