Radioactivity
Lecture 5 The Nature and Laws of Radioactivity
Changing Z to N or N to Z Adding a proton (electron) Subtracting or adding neutrons
nucleus becomes unstable and decays by internally converting Carbon to Nitrogen neutrons to protons (beta-decay)!
Gold to Mercury
What are the physical laws that govern the decay process? Terminology of nuclear decay
Time dependent change from configuration 1 (radioactive nucleus) To configuration 2 (decay product, daughter)
Activity: number of decay events per time Decay constant: probability of decay Half life: time for the activity to be reduced to 50%
Activity corresponds to the number of sand particles dripping through hole Decay constant is associated with the size of the hole Units for the Activity A for a radioactive nucleus Classical unit: Curie: Ci corresponds to the number of decays of 1 g Radium as introduced by Madame Curie Modern unit: Becquerel: Bq notes a single decay event 1 Ci = 3.7·1010 decays/s = 3.7·1010 Bq
1 Bq = 1 decay/s
Example: the human body is radioactive with and activity of: 2.210-7Ci = 0.22Ci 8000 Bq = 8 kBq Sounds comfortably low sounds alarmingly high Radioactive Decay Law
Describes the change of activity with time
1000.0 900.0 800.0 t =100 years 700.0 1/2 t 600.0 Amother(t) A0 e 500.0 400.0 t 300.0 A (t) A 1 e abundance/activity daughter 0 200.0 100.0 0.0 0 200 400 600 800 1000 1200 λ≡decay constant; time [years] a natural constant exponential decay with time! for each radioactive At half life 50% of the activity is gone! element. Half life: t1/2 = ln2/λ 1st example: 22Na 22Na is a radioactive nucleus with a half-life of 2.6 years, what is the decay constant? Mass number A=22; (don’t confuse with activity A(t)!)
ln 2 ln 2 0.27 y 1 : t1/ 2 2.6 y 1 y 3.14107 s 107 s
ln 2 8.5109 s1 2.63.14107 s Radioactive Decay Laws Activity of radioactive substance A(t) is at any time t proportional to number of radioactive particles N(t) :
A(t) = ·N(t)
A 22Na source has an activity of 1 Ci = 10-6 Ci, how many 22Na nuclei are contained in the source? (1 Ci = 3.7·1010 decays/s)
A 106 Ci 106 3.71010 s1 N 4.361012 8.5109 s1 8.5109 s1 How many grams of 22Na are in the source?
An amount of A grams of atoms with the
mass number A (1mole) contains NA nuclei
23 NA ≡ Avogadro’s Number = 6.023·10 nuclei/mole
➱ 22g of 22Na contains 6.023·1023 nuclei
N22Na 4.361012 particles 6.0231023 1g particles 22 224.361012 N22Na g 1.591010 g 6.0231023 t N(t) N0 e How many particles are in the source after 1 y, 2 y, 10 y?
1 N(t) 4.361012 e0.27y t A(t) N(t) 8.5109 s1 N(t)
1 N(1y) 4.361012 e0.27y 1y 3.331012 A(1y) 28305s1 0.765Ci
1 N(2y) 4.361012 e0.27y 2 y 2.541012 A(2y) 21590 s1 0.58Ci
1 N(10y) 4.361012 e0.27y 10y 2.931011 A(10y) 2490.5s1 0.067Ci
Decay in particle number and corresponding activity! 2nd example: Radioactive Decay Plutonium 239Pu, has a half life of 24,360 years. 1. What is the decay constant? 2. How much of 1kg 239Pu is left after t=100, 1,000, 10,000, 24,360, 100,000years? ln 2 ln 2 2.85105 y 1 t1/ 2 24360y
t 2.85105 y1100y N 239 (t) N e N 239 (100y) 1kge Pu 0 Pu
N 239 (100y) 0.9972kg Pu
N 239Pu (1,000y) 0.9719kg
N 239 (10,000y) 0.7520kg Pu
N 239Pu (24,360y) 0.5kg
N 239 (100,000y) 0.0578kg Pu From parent to daughter nuclei 14 14 N0 C N T1/2=5,730 y
22 22 N2 (daughter) Na Ne T1/2=2.6 y
26Al 26Mg N1 (parent) T1/2=716,000 y
40K40Ar
T1/2=1,280,000,000 y
N0 N1 N2 , N2 N0 N1 t The initial radioactive nuclei slowly decay with N1 N0 e time converting the initial radioactive species t to non radioactive material N2 N0 (1 e ) 3rd example: determine the number of daughter nuclei
Assume a mix of 100 nuclei of 14C, 22Na, 26Al, and 40K each. Calculate the number of daughter nuclei after: t1=10 y, t2=10,000 y, t3=10,000,000 y and t4=10,000,000,000 y
ln2 t t T1/ 2 N2 N0 (1 e ) N0 (1 e )
t 10y 10000 y 10000000 y 10000000000 y
T1/2 l 14N 5730 1.21E-04 1.21E-01 7.02E+01 1.00E+02 1.00E+02 22Na 2.6 2.67E-01 9.30E+01 1.00E+02 1.00E+02 1.00E+02 26Al 716000 9.68E-07 9.68E-04 9.63E-01 1.00E+02 1.00E+02 40K 1280000000 5.42E-10 5.42E-07 5.42E-04 5.40E-01 9.95E+01