Exploring 99Tc: Understanding Radioactive Decay and Half-Life

[conniechiwa]

Homework Statement

*I'm only stuck on part c

During the testing process for some pharmaceuticals, the drug is "tagged" with a radioactive material. This way researchers can determine if the pharmaceutical is going to other parts of the body than the intended target and what effect it has on the non-target areas. By adding this radioactive tag to the pharmaceutical, researchers can pinpoint all parts of the body and the concentration that accumulates in non-target areas.

One possible such tag is technetium-99, 99Tc, which has a half-life of 6.05 hours.
a) How many 99Tc nuclei are required to give an activity of 1.6 μCi?
Answer: 1860176361

b) What is the decay constant for this isotope?
Answer: 0.11457 hour-1

c) Suppose the drug containing the amount of 99Tc calculated in part (a), were injected into the patient 1.5 hours after it was prepared, what would its activity be at that time?

Homework Equations

N=N0e^-λt
R=λN0
λ=ln2/T1/2

The Attempt at a Solution

N=N0e^-λt
N=(1860176361)e^-(0.11457 hour-1)(1.5 hours)
N=1566456874

λ=ln2/T1/2
λ=ln2/(6.05 hours* 60min/hour * 60 sec/min)
λ=3.18249E-5 hour-1

R=λN0
R=(3.18249E-5 hour-1)(1566456874)
R=49852.39512 Ci

I'm not sure what I did wrong...

 

[conniechiwa]

Nevermind. I ended up figuring out my mistake.

 

[baba89]

Your calculations for part a and b seem to be correct. For part c, you have correctly used the decay constant and the time elapsed to calculate the remaining number of nuclei, which is 1566456874. However, the activity is not equal to the number of nuclei. Activity is defined as the rate at which nuclei decay, and it is measured in units of becquerel (Bq) or curie (Ci). It is equal to the decay constant multiplied by the number of nuclei present. So, to calculate the activity at 1.5 hours, you need to use the formula R=λN, where R is the activity, λ is the decay constant (3.18249E-5 hour-1), and N is the number of nuclei (1566456874). This will give you a result of 49.85 Ci, which is the activity of the drug at 1.5 hours after it was prepared.