Problem: Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?

FREE Expert Solution

We’re being asked to calculate the percent of the radioactivity that would remain for each of the isotopes after 2 days (48 h).


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

ln [N]t=-kt+ln [N]0

where:

[N]t = concentration at time, t
k = decay constant
t = time
[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half

The half-life of a first-order reaction is given by:

t12=ln 2k


For technetium-99:

We first need to calculate for the decay constant using the given half-life of technetium-99, 6 hours:

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Problem Details

Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?

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