RADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 101º Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 2 and isotop half-life T1/2: In(2) 0.693 Radioisotope Half-life Modality T1/2 T1/2 Carbon-11 20 minutes PET where a is decay constant (1/s), T1/2 is isotope half- life (s). 3. Activity or decay rate of a radioactive source A: ΔΝ Fluorine-18 110 minutes PET Copper-64 12.7 hours PET Gallium-67 78.3 hours SPECT Gallium-68 68 minutes PET = AN Technetum-99m 6.02 hours SPECT Δt where A is activity or decay rate of a radioactive source (Bq), N is number of nuclei present at time t (s ), 1 is decay constant (1/s). 4. Activity A of a radioactive source at a time t: Indium-111 67,3 hours SPECT lodine-123 13.22 hours SPEC Thallium-201 72,9 hours SPECT A = Aoe¬at = A,2 ™1/2 A, is initial activity (Bq), T/2 half life time of an isotope (s). 5. Relationship between mass and number of nuclei: т M NA m is mass (kg), M is molar mass (kg/mole), N is number of nuclei, N, = 6.022 · 1023 mole"! is Avogadro's constant. 10. Iodine-120 has a half life of 1.35 hours. If you start off with a sample which has an activity of 1.0 Ci, how long is it before the activity drops to the following values: (a) 0.50 Ci; (b) 9.77×10 Ci; (c) 9.31×10¯1º Ci.
RADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 101º Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 2 and isotop half-life T1/2: In(2) 0.693 Radioisotope Half-life Modality T1/2 T1/2 Carbon-11 20 minutes PET where a is decay constant (1/s), T1/2 is isotope half- life (s). 3. Activity or decay rate of a radioactive source A: ΔΝ Fluorine-18 110 minutes PET Copper-64 12.7 hours PET Gallium-67 78.3 hours SPECT Gallium-68 68 minutes PET = AN Technetum-99m 6.02 hours SPECT Δt where A is activity or decay rate of a radioactive source (Bq), N is number of nuclei present at time t (s ), 1 is decay constant (1/s). 4. Activity A of a radioactive source at a time t: Indium-111 67,3 hours SPECT lodine-123 13.22 hours SPEC Thallium-201 72,9 hours SPECT A = Aoe¬at = A,2 ™1/2 A, is initial activity (Bq), T/2 half life time of an isotope (s). 5. Relationship between mass and number of nuclei: т M NA m is mass (kg), M is molar mass (kg/mole), N is number of nuclei, N, = 6.022 · 1023 mole"! is Avogadro's constant. 10. Iodine-120 has a half life of 1.35 hours. If you start off with a sample which has an activity of 1.0 Ci, how long is it before the activity drops to the following values: (a) 0.50 Ci; (b) 9.77×10 Ci; (c) 9.31×10¯1º Ci.
Chapter11: Nuclear Physics
Section: Chapter Questions
Problem 4Q
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Question
Transcribed Image Text:RADIOACTIVITY. LAW OF RADIOACTIVE DECAY
Activity units:
1 Ci = 3.7 × 101º Bq
1. Nuclear decay law:
N = Noe¬at,
The law of radioactive decay gives the quantitative relationship between the original number
of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828...
is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s).
2. Relationship between decay constant 2 and isotop half-life T1/2:
In(2)
0.693
Radioisotope
Half-life
Modality
T1/2
T1/2
Carbon-11
20 minutes
PET
where a is decay constant (1/s), T1/2 is isotope half-
life (s).
3. Activity or decay rate of a radioactive source A:
ΔΝ
Fluorine-18
110 minutes
PET
Copper-64
12.7 hours
PET
Gallium-67
78.3 hours
SPECT
Gallium-68
68 minutes
PET
= AN
Technetum-99m
6.02 hours
SPECT
Δt
where A is activity or decay rate of a radioactive
source (Bq), N is number of nuclei present at time t
(s ), 1 is decay constant (1/s).
4. Activity A of a radioactive source at a time t:
Indium-111
67,3 hours
SPECT
lodine-123
13.22 hours
SPEC
Thallium-201
72,9 hours
SPECT
A = Aoe¬at = A,2 ™1/2
A, is initial activity (Bq), T/2 half life time of an isotope (s).
5. Relationship between mass and number of nuclei:
т
M NA
m is mass (kg), M is molar mass (kg/mole), N is number of nuclei, N, = 6.022 · 1023 mole"!
is Avogadro's constant.
Transcribed Image Text:10. Iodine-120 has a half life of 1.35 hours. If you start off with a sample which has an
activity of 1.0 Ci, how long is it before the activity drops to the following values: (a) 0.50 Ci;
(b) 9.77×10 Ci; (c) 9.31×10¯1º Ci.
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