Radioactive gold-198 is used in the diagnosis of liver problems. 198Au decays in a first-order process, emitting a β particle (electron). The half-life of this isotope is 2.7 days. You begin with a 5.6-mg sample of the isotope. Calculate how much gold-198 remains after 3.0 days.

2.576 mg of gold-198 remains after 3 days

Explanation:

N = No(0.5)^t/t1/2

No is the initial amount of gold-198 = 5.6 mg

t is the time taken for gold-198 to reduce to a certain amount (N) = 3 days

t1/2 is the half-life of gold-198 = 2.7 days

N = 5.6(0.5)^3/2.7 = 5.6(0.5)^1.11 = 5.6×0.46 = 2.576 mg

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