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 3 of 3: Decay to 1 %

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t = \dfrac{\ln(A_0/A)}{\lambda} = \dfrac{\ln 100}{3.20\times 10^{-5}} = 1.44\times 10^{5}\ \text{s} = 39.9\ \text{h}

Analysis

$A = A_0 e^{-\lambda t}$ gives $t = \ln(200/2)/\lambda = \ln 100/\lambda$ . With $\lambda = 3.209\times 10^{-5}$ s $^{-1}$ , $t = 1.435\times 10^{5}$ s $\approx 39.9$ h, i.e. about $\ln 100/\ln 2 = 6.64$ half-lives.