The rate of radioactive decay follows first-order kinetics where the rate of decay is proportional to the number of radioactive nuclei (N) in the sample as expressed in Equation 6.1 where k is called the nuclear decay constant. Rate = kN (Equation 6.1) Equation 6.1 can be transformed into Equation 6.2 where No is the initial number of nuclei at initial time, time =0, and N. is the number of nuclei after time a certain time interval, t. Nt In = -kt (Equation 6.2) No A more useful way of determining the rate of radioactive decay is by determining the half- life of a radioisotope. Half-life (t1/2) is the time required for half of any given quantity of radioactive substance to decay. Each radioisotope has a characteristic half-life. For example, cobalt-60 which is used for cancer radiation therapy has a half-life of 5.3 years. So for a 1.00 g sample of cobalt-60 it will take 5.3 years before its amount is reduced to 0.500 g and 10.6 yrs to 0.250g and so on and so forth. Equation 6.3 gives the general equation for the half-life of any radioactive substance while Equation 6.4 the general formula in calculating the amount of remaining substance after n half-lives. t1/2 = (Equation 6.3) 0.693 k Nt= (1/2) No (Equation 6.4)
The rate of radioactive decay follows first-order kinetics where the rate of decay is proportional to the number of radioactive nuclei (N) in the sample as expressed in Equation 6.1 where k is called the nuclear decay constant. Rate = kN (Equation 6.1) Equation 6.1 can be transformed into Equation 6.2 where No is the initial number of nuclei at initial time, time =0, and N. is the number of nuclei after time a certain time interval, t. Nt In = -kt (Equation 6.2) No A more useful way of determining the rate of radioactive decay is by determining the half- life of a radioisotope. Half-life (t1/2) is the time required for half of any given quantity of radioactive substance to decay. Each radioisotope has a characteristic half-life. For example, cobalt-60 which is used for cancer radiation therapy has a half-life of 5.3 years. So for a 1.00 g sample of cobalt-60 it will take 5.3 years before its amount is reduced to 0.500 g and 10.6 yrs to 0.250g and so on and so forth. Equation 6.3 gives the general equation for the half-life of any radioactive substance while Equation 6.4 the general formula in calculating the amount of remaining substance after n half-lives. t1/2 = (Equation 6.3) 0.693 k Nt= (1/2) No (Equation 6.4)
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:The rate of radioactive decay follows first-order kinetics where the rate of decay is
proportional to the number of radioactive nuclei (N) in the sample as expressed in Equation 6.1
where k is called the nuclear decay constant.
Rate = kN (Equation 6.1)
Equation 6.1 can be transformed into Equation 6.2 where No is the initial number of nuclei at initial
time, time =0, and N₁ is the number of nuclei after time a certain time interval, t.
In = -kt (Equation 6.2)
Nt
No
A more useful way of determining the rate of radioactive decay is by determining the half-
life of a radioisotope. Half-life (t₁/2) is the time required for half of any given quantity of radioactive
substance to decay. Each radioisotope has a characteristic half-life. For example, cobalt-60
which is used for cancer radiation therapy has a half-life of 5.3 years. So for a 1.00 g sample of
cobalt-60 it will take 5.3 years before its amount is reduced to 0.500 g and 10.6 yrs to 0.250g and
so on and so forth. Equation 6.3 gives the general equation for the half-life of any radioactive
substance while Equation 6.4 is the general formula in calculating the amount of remaining
substance after n half-lives.
0.693
t1/2 =
(Equation 6.3)
Nt= (1/2) No (Equation 6.4)
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