Question

Cesium-131 is the latest tool of nuclear medicine. It is used to treat malignant tumors by implanting Cs-131 directly into the tumor site. Its first-order half-life is 9.7 days. If a patient is implanted with 20.0 mg of Cs-131, how long will it take for 13% of the isotope to remain in his system?

Answer 1

Cesium-131 is the latest tool of nuclear medicine. It is used to treat malignant tumors by implanting Cs-131 directly into the tumor site. Its first-order half-life is 9.7 days. If a patient is implanted with 20.0 mg of Cs-131, how long will it take for 13% of the isotope to remain in his system?

1)T1/2=9.7 days

Using equation for first order equation,

ln([C]t/[C]o)=-kt

where Ct= concentration after t

Co=initial concentration

At t1/2, ct=co/2

So ln ½=-kt

T1/2=0.693/K

K=rate constant

K=0.693/t1/2=0.693/9.7=0.0714 day^-1

2) ln([C]t/[C]o)=-kt

[C]o=20mg

[C]t=13% *20.0 mg=0.13*20.0=2.6 mg

T=?

T=-1/K( ln([C]t/[C]o)=-1/0.0714 day-1(ln 13/20)=-1/0.0714*ln 0.65=6.0 days

T=6.0days