# 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:

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:

For technetium-99:

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

90% (406 ratings) ###### 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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Our tutors have indicated that to solve this problem you will need to apply the Integrated Rate Law concept. You can view video lessons to learn Integrated Rate Law. Or if you need more Integrated Rate Law practice, you can also practice Integrated Rate Law practice problems.

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Based on our data, we think this problem is relevant for Professor Scholefield's class at SMC.

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