The value of k if 94 % of the technetium has decayed after 24 hours (that is, 6 % remains) when the amount of 99 m Tc decays exponentially according to the model Q t = Q 0 e − k t .
The value of k if 94 % of the technetium has decayed after 24 hours (that is, 6 % remains) when the amount of 99 m Tc decays exponentially according to the model Q t = Q 0 e − k t .
Solution Summary: The author explains how 99mTc decays exponentially according to the model Q(t)=Q_0e-kt.
To determine: The value of k if 94% of the technetium has decayed after 24 hours (that is, 6% remains) when the amount of 99mTc decays exponentially according to the model Qt=Q0e−kt .
(b)
To determine
To determine: The amount remaining after 10 hours if 30 mCi is initially given to a patient for blood pool imaging of the heart when the amount of 99mTc decays exponentially according to the model Qt=Q0e−kt .
(c)
To determine
To determine: The amount of time required for the amount of 99mTc to fall below 1% of the original amount when the amount of 99mTc decays exponentially according to the model Qt=Q0e−kt .
An archaeological sample contains 0.622 g of lead-206 and 2.198 g of uranium-238. Assume that all the lead now present in the rock came from the radioactive decay of the
uranium and that no appreciable amounts of other radioactive nuclides are present in the sample. The decay rate constant for the uranium is 1.54 x 10-10
of the sample?
year. What is the age
O a.9.1 x 109 years
O b.7
7.98 x 108 years
OC 1.84 × 109 years
O d. 7.26 x 109 years
O e. none of these
Technetium-99m (abbreviated 99m Tc) is a short-lived gamma-ray emitter that is used in nuclear medicine. Suppose that a patient is given a small amount of 99m Tc for a diagnostic test. Further suppose that the amount of 99m Tc decays exponentially according to the model Q(t) = Q0e−kt. The value Q0 is the initial amount administered, and Q(t) represents the amount of 99m Tc remaining after t hours. The value of k is the decay constant.
a. If 94% of the technetium has decayed after 24 hr (that is, 6% remains), determine the value of k. Round to 3 decimal places.
b. If 30 mCi is initially given to a patient for blood pool imaging of the heart, determine the amount remaining after 10 hr. Round to 1 decimal place.
c. Determine the amount of time required for the amount of 99m Tc to fall below 1% of the original amount given. Round to 1 decimal place.
Initially, 10 grams of a radioactive substance were found in a sample. It was observed
that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams
remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one-
half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is
In z
1
2
0.7
proportional to the amount of the substance present at time t. You must begin your solution process by
3
considering the proportional relationship presented below. Use the natural logarithm table to the right
1.1
to provide an approximate answer. Your work must support your answer.
4
1.4
1.6
dA
a A
6
1.8
dt
1.9
2.1
9
2.2
10
2.3
7,
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