Radioactivity Yoichi Watanabe, Ph.D. Masonic Memorial Building M10-M Telephone: (612)626-6708 E-mail: [email protected] http://www.tc.umn.edu/~watan016/Teaching.htm MPHY 5174 Spring Semester

Outline I. Radioactivity II. Modes of Radioactive Decays III. Decay of Radioactivity

Antonio Henri Becquerel 

Henri Becquerel (1852-1908) noticed black spots on a photographic plate with uranium salts and pure uranium metal in 1896.

Marie and Pierre Curie   

Pierre Curie (1859-1906) and Marie Curie (1867-1934) coined the term Radioactivity. They studied radioactivity using uranium ore after the discovery of Becquerel. They discovered Polonium and Radium.

Radioactivity All elements with Z greater than 82 are radioactive. (82Pb) => natural radioactivity.  There is at least one stable configuration in atoms lighter than and equal to Z = 82.  Radioactive isotopes can be produced by bombarding stable nuclei with particles, (i.e., neutrons, high energy protons, etc.) => artificial radioactivity. 

Radium  

 

Radium is the sixth member of the naturally occurring uranium series. Radium nuclides contain 88 protons (Z=88). The most stable radium isotope is 226Ra, which contains 136 neutrons (A=226). 226Ra disintegrates to form Radon. Radium was used to treat cancer by placing it near or in contact with a tumor soon after the discovery of Radium by the Curies.

226 88

Ra  → Rn 222 86

Outline I. Radioactivity II. Modes of Radioactive Decays III. Decay of Radioactivity

Modes of Radioactive Decay  

Alpha (α) particle decay Beta (β) particle decay  

  

Negatron (electron) emission, β− decay Positron emission, β+ decay

Electron capture (EC) Gamma (γ) emission Internal conversion  

Auger electron Isomeric transition

Spontaneous fission

Alpha particle decay (1) 



 

A nucleus emits alpha (α) particle, which is positively charged by loosing two atomic electrons from an helium atom. α particle is a helium nucleus, whose atomic number is 2 and mass number is 4. It is composed of two neutrons and two protons. Heavy nuclei (i.e., nuclides with A > 150) tend to decay via α-decay. 238U, 226Ra, and 222Rn are α particle emitters.

Alpha particle decay (2) A Z

X→

A− 4 Z −2

Y + He + Q 4 2

Q = [M P − ( M D + M α )]c 226 88

2

Ra 1622 a → Rn + He + 4.87 MeV 222 86

4 2

Energy Level Diagram: 226Ra 226Ra 88

α2 (5.5%), 4.60 MeV

γ, 0.18 MeV

222Rn 86

α1 (94.5%), 4.78 MeV

Proton and neutron do decay  

The half-life of neutron is 886.7±1.9 s (14.77min). The half-life of proton is longer than 1025 years.

n → p + e +ν −

p → e +π +

0

p → n + e +ν +

−

Beta minus decay: β decay − A A + +Q Z X → Z +1Y + 2 2 M P c = M D c + Te − + Tν

β

32 15

ν

  → S + β +ν + 1.71 MeV P 14 .3 days 32 16

−

Total kinetic energy of β and ν.

Energy Level Diagram: 32P 32P 15

β− (100%), Emax=1.71 MeV 32S 16

Energy Level Diagram: 14C 14C 6

β− (100%), Emax=0.156 MeV 14N 7

+

Beta plus decay: β decay A A Z X → Z −1Y

+

+ β +ν + Q

M P c = M D c + 2me c + Te + Tν 2

2

2

+

22 11

 → Ne + β +ν + 1.82 MeV Na 2 .6 years

13 7

+

22 10

 → C + β +ν + 2.21MeV N 10 .0 min 13 6

+

Energy Level Diagram: 13N 13N 7

2 x 0.511 MeV 2.21 MeV β+ , Emax=1.19MeV 13C 6

Energy Level Diagram: 15O 15O

8

2 x 0.511 MeV 2.722 MeV β+ , Emax=1.7MeV 15N 7

Energy Level Diagram: 18F 18F 9

2 x 0.511 MeV 1.655 MeV β+ , Emax=0.633 MeV 18O

8

Why is 2mec2 in the diagram? 13 7

 → C + β +ν + 2.21MeV N 10 .0 min 13 6

+

Mass of 13N nucleus = Aw(13N) - 7mec2 Mass of 13C nucleus = Aw(13C) - 6mec2 LHS = Aw(13N) - 7mec2 RHS = Aw(13C) - 6mec2 + mec2 + Tβ+Tν Hence, Aw(13N) = Aw(13C) + 2mec2 + Tβ+Tν Aw = Atomic weight

Energy Spectrum of β  

 

The excess nuclear energy of the reaction is shared between β and (anti) neutrino. The energy spectrum of β particles is the bellshaped continuous distribution with the maximum. The average energy of β− particles is about 1/3rd of the maximum energy. The low energy part of electron spectra is enhanced and that of positron spectra is held back.

Energy Level Diagram: 64Cu 64Cu 29

EC (40.5%)

T1/2=12.70 h

β- (40%),Emax=0.571MeV

EC(0.6%) 64Zn 30

γ, 1.3461 MeV

64Ni 28

β+ (19.3%), Emax=0.657MeV

Beta ray spectra: 64Cu

Number of β per unit energy

5 4

β+

3 2

β-

1 0 0

0.1

0.2

0.3

0.4

0.5

Kinetic energy [MeV]

0.6

0.7

Beta ray spectra: 64Cu R.D.Evans, The Atomic Nucleus, page 538 Figs1.3-1.6

Positron Emission Tomography PET uses 0.511 MeV photons, produced by electron-positron annihilation.  PET needs radioisotopes, which emit positrons through β+ decay.  Photons are detected by many photomultiplier tubes.  Tomographic image is reconstructed. 

Siemens PET-CT

PET Isotopes Nuclides

T1/2

Production

Carbon-11

20.4 min

10B(d,n)11C

Nitroten-13

9.96 min

12C(d,n)13N

Oxygen-15

2.05 min

14N(d,n)15O 16O(p,pn)15O 12C(α,n)15O

Fluorine-18

110 min

18O(p,n)18F

Copper-64

12.7 hrs

64Ni(p,n)64Cu

Electron Capture (EC)   



An orbital electron is captured by a nucleus. Often EC involves the K-shell electron (K capture). The characteristic X-ray is emitted when the orbital electron in a higher energy level falls to the hole in the Kshell. The characteristic X-ray photon may be absorbed by the atom, causing emission of electrons, Auger electron. −

p + e → n +ν

A Z X

A + e→ Z −1Y

+ν + Q

M P c 2 = M D c 2 + E B + Tν

Electron Capture (2) Characteristic x-ray electrons

electrons

K-shell Z, N

N+1 Z-1

Energy of x-ray = EL - EK

Energy Level Diagram: 125I 125I

EC(100%)

53

60.2 d 0.177 MeV

γ or IC (0.03546MeV) 125Te 52

Energy Level Diagram: 18F 18F 9

EC

2 x 0.511 MeV

1.655 MeV β+ , Emax=0.633 MeV 18O

8

Energy Level Diagram: 22Na 22Na 11

β+ (90.4%),Emax=0.54MeV 2 x 0.511 MeV EC(9.5%)

β+ (0.06%), Emax=1.83MeV

(1.27MeV)

22Ne 10

Gamma Emission Upon radioactive decay (α,β,or EC), a nucleus is left in an excited state.  The excited state transits to the ground state by emitting gamma ray or internal conversion.  The gamma emitting nuclides are the major source of gamma rays used for radiation therapy. 

Energy Level Diagram: 133Xe 133Xe 54

β1− ( 0.006%), Emax=0.043 MeV 0.384 MeV β2− ( 0.7%), Emax=0.266 MeV

γ

β3− (99.2%), Emax=0.346 MeV

0.161 MeV 0.081 MeV 0.0 133Cs

55

0.427 MeV

Internal conversion (1) It is “internal photoelectric effect”.  A nucleus in an excited state transfers the energy to one of orbital electrons.  The electron, conversion electron, is ejected from the atom.  Internal conversion causes emission of characteristic x-ray or Auger electrons. 

Internal conversion (2) Electron electrons

electrons

K-shell

γ

Z, N

N-1 Z+1 Excited state

β- decay Energy of ejected electron = Eγ - EK

Energy Level Diagram: 137Cs 137Cs

55

β1− (94.6%), Emax=0.514 MeV 137mBa , 56

β2− (5.4%), Emax=1.176 MeV

T1/2=2.55m

γ (85%), 0.662 MeV IC, K(7.7%), L(1.4%), M(0.5%)

137Ba 56

Auger Electrons (1) A hole is created in the K, L, or M shell after an electron is ejected from an atom by electron capture or a high energy charged particle or internal conversion.  The hole is filled with an electron jumping from a higher energy shell (or level) with an emission of characteristic x-ray.  Instead of x-ray, an electron in a higher energy level, Auger electron, can be ejected. 

Auger Electrons (2) Auger electron

M-shell L-shell K-shell

X-ray

hole Energy of x-ray = EK – EL Energy of Auger electron = (EK – EL) – EM

Isomeric transition   

An excited nucleus is in metastable state. The nucleus is called isomer and it is in an isomeric state. The transition to the ground state is called an isomeric transition.



99mTc

is isomer of 99Tc. Its half life is 6 hours.

Energy Level Diagram: 137Cs 137Cs

55

β1− (94.6%), Emax=0.514 MeV 137mBa , 56

β2− (5.4%), Emax=1.176 MeV

T1/2=2.55m

γ (85%), 0.662 MeV IC, K(7.7%), L(1.4%), M(0.5%)

137Ba 56

Spontaneous Fission Heavy nuclides undergo spontaneous fission decay. The nuclides break into two heavy nuclides naturally.  Cf-252 decays through spontaneous fission process with T1/2=2.645 years. It has been used as a neutron source. One of medical applications is for neutron therapy. 

Chart of Nuclides (1)

Z

N

http://ie.lbl.gov/toi/pdf/chart.pdf

Chart of Nuclides (2)

Outline I. Radioactivity II. Modes of Radioactive Decays III. Decay of Radioactivity

Decay Constant, λ 

The number of nuclides disintegrating per unit time (∆N/∆t) is proportional to the number of radioactive nuclides (N):

dN dN = − λ N = −λN dt dt

Activity 

The rate of decay is the activity, A, of a radioactive nuclide.

A = λN The unit of activity is Becquerel (Bq). One Bq means one disintegration per second (dps). 1 Ci is 3.7x1010 dps and it is based on the activity of 1 g of radium.

A Solution of Decay Equation N (t ) = N (0)e

A(t ) = A(0)e−λt

− λt

Acitivity, MBq

Carbon 10 1000 900 800 700 600 500 400 300 200 100 0

T1/2 = 19.3 s

0

5

10

15

20

Time, Seconds

25

30

Half-life 

Time for activity to decrease to a half.

A(T1/ 2 ) = A(0)e

A(0) 1 = A(T1/ 2 ) 2

−λ T1 / 2

T1/ 2 =

0.693

ln( 2)

λ

Half-life of Radionuclides in Nuclear Medicine

J.T.Bushberg et al, Essential Phys of Med Imaging, 2nd ed.

Decay Factor (DF) and Table A(t) = 𝐴𝐴(0)𝑒𝑒 −0.693𝑡𝑡/𝑇𝑇1⁄2

D𝐹𝐹 = 𝑒𝑒

−0.693𝑡𝑡/𝑇𝑇1⁄2

Example: A vial containing 90mTC is labeled “2 (T1/ 2 ) = mCi/ml at 8 am.” What volume A should be withdrawn at 4 pm on the same day to prepare an injection of 1.5mCi for a patient?

A(0)e − λ T1 / 2

After 8 hours, DF = 0.397 (Table 4-1). So, to get 1.5mCi, one needs 1.5/(2*0.397) = 1.89 ml. Cherry et al, Phys in Nucl Med, 4th ed.

Average life 

The number of disintegrations in the mean (or average) life is equal to the number of disintegrations in the infinite time.

∞ ∫0

A(t )dt = A(0)Ta Ta = 1.44T1/ 2

Specific Activity  





Activity per unit mass, Ci/g. A radioactive source may contain stable isotopes of the radionuclide of interest (with carrier). A pure radionuclide is called as carrierfree. The highest specific activity is that of the carrierfree radionuclide and it is called as carrier-free specific activity (CFSA). A specific activity is desirable for nuclear medicine applications.

Radioactivity Example 1 1. 2.

The number of atoms in 1 g of 226Ra. The activity of 1 g of 226Ra.

 N A ⋅ m = AW   N ⋅m = M

(A1) The atomic weight is the mass in gram of NA atoms. Here NA is the Avogadro’s number.

N AM 6.022 × 10 23 × 1 = = 2.664 × 10 21 N= 226.025 AW

(A2) T1/2 of 226Ra=1600 years.

0.693 = 1.373 × 10 −11s −1 1600 × 365 × 24 × 60 × 60 A = λN = 3.658 × 1010 dps ≅ 1Ci

λ=

Radioactivity Example 2 1.

When will 5 mCi of 131I and 2 mCi of 32P have equal activities? (A1) T1/2 of 131 I is 8.040 days. T1/2 of 32P is 14.28 days.

I 0e

− λI t

= P0e

− λP t

1 I0 t= ln λI − λ p P0

λI=0.0862 day-1 λP=0.0485 day-1 t=24.3 days

Radioactive Series  

The product of parent radioactive nuclide, daughter, may be also radioactive. There is a chain of decaying nuclides. λ1

λ2

λ3

N1 ⇒ N 2 ⇒ N 3 ⇒ What is the relation between activities of three nuclides?

Decay Series Diagram Isotope T1/2 [years] 238U

4.5x109

234U

2.5x105

230Th

7.5x104

226Ra

1600

222Rn

3.82 days

206Pb

stable

Bateman equations dN1 = −λ1 N1 dt

N1 (t ) = N1 (0)e −λ1t

Eq.(1)

Eq.(4)

dN2 = λ1 N1 − λ2 N 2 dt

λ1 −(λ2 −λ1 )t { } N ) = ( ) 1 − e Eq.(5) ( t N t 1 Eq.( 2) 2 λ2 − λ1

dN3 = λ2 N 2 − λ3 N 3 dt

Eq.(3)

N 3 (t ) = ..... Eq.(6)

Equation (5) A2 (t ) = A1 (t )

λ2

λ2

{ 1− e −λ

−( λ2 −λ1 )t

}

1

T1  A2 (t ) = A1 (t ) 1 − e T1 − T2  

T1 −T2 −0.693 t T1T2 

 

Radioactive Equilibrium: Transient equilibrium

if T1 > T2 A2 (t ) T1 = A1 (t ) T1 − T2 The daughter nuclide decays with the decay constant of the parent.

A

Molybdenum-99 generator Mo99 Tc99m Tc99m after "milking"

100 90 80 70 60 50 40 30 20 10 0

T1/2: 99Mo

= 67 hours 99mTc = 6 hours

0

20

40

60

80 100 120

Hours Notes: only 87% of Mo-99 decays to Tc-99m. 13% decays directly to Tc-99.

Radioactive Equilibrium: Secular equilibrium

if T1 >> T2 A2 (t ) = A1 (t ) λ1 N1 = λ2 N 2 = λ3 N 3 = ....

A

Radium-226 Source 100 90 80 70 60 50 40 30 20 10 0

Ra226 Rn222

0

20

40

60

Days

80 100 120

T1/2: 226Ra

= 1600 years 222Rn = 3.824 days