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] =

number of molecules / avogadro's number * molecule molecular = mass

explanation:

we define a gram-molecular weight as the mass of one mole of any element or compound. a mole contains avogadro's number of units (molecules) –  

6.022

x

10

23

. so, dividing the number of molecules by avogadro's number gives us the number of moles. multiplying that by the molecular weight gives us the mass. from the periodic table we find the gram-molecular weight of u to be238 and of f to be19. so,  

u

f

6

will have a gram-molecular weight of 352g.