Problem 1

Molecular imaging is a powerful tool in medical diagnostics. The nuclear isomer

^{99m}\ce{Tc}

(m = metastable) is an excellent γ-emitter (

t_{1/2} = 6.015

h) obtained by β− decay of a mother nuclide in a technetium generator as

[^{99m}\ce{TcO4}]^-

. (a) Identify the mother nuclide A and the emitted particle B in

\ce{A -> ^{99m}Tc + B}

. (b) An eluate from a

^{99m}\ce{Tc}

generator has an activity of 12.5 GBq (1 GBq =

10^{9}

decays per second). Calculate how many moles of

^{99m}\ce{Tc}

are present. (c) For standard imaging about 200 MBq are administered to a patient. Assuming no activity is lost through excretion, calculate how many hours the patient has to wait until the injected activity decreases to under 1% of the starting activity.

Step 2 of 3: Moles from activity

← Previous Next →

Intuition

Activity counts decays per second; dividing by the decay constant gives the number of atoms, and dividing by Avogadro's number gives moles.

n = \dfrac{A}{\lambda N_A} = \dfrac{12.5\times 10^{9}}{(0.693/21660)\times 6.022\times 10^{23}} = 6.5\times 10^{-10}\ \text{mol}

Analysis

With $t_{1/2} = 6.015$ h $= 21654$ s, $\lambda = \ln 2/t_{1/2} = 3.20\times 10^{-5}$ s $^{-1}$ . Then $N = A/\lambda = 12.5\times 10^{9}/3.20\times 10^{-5} = 3.9\times 10^{14}$ atoms, i.e. $n = N/N_A = 6.5\times 10^{-10}$ mol of $^{99m}\ce{Tc}$ .