The technetium-99 isotope has a half-life of 6.0 hours. If 100.0 mg were injected into a patient how much remains after 18 hours?

12.5mg of technetium-99 remain

Explanation:

When a radioactive isotope decays in the time, its concentration follows the equation:

ln[A] = -kt + ln[A]₀

Where [A] could be taken as the mass of radioactive isotope after time t (18h),

k is rate constant = ln 2 / Half-Life = ln 2 / 6hours = 0.1155hours⁻¹

[A]₀ is initial amount of the isotope = 100.0mg

Replacing:

ln[A] = -0.1155hours⁻¹ *18hours+ ln[100.0mg]

ln[A] = 2.5257

[A] =

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