Chapter 1: Radioactivity

Chapter 1: Radioactivity

35 NPRE 441, Principles of Protection Chapter 1: Radioactivity

Radioactivity

• Radioactivity is defined as the spontaneous nuclear transformation that results in the formation of new elements.

• Radioactivity and radioactive properties of are determined by nuclear considerations and independent of chemical and physical states of the radioisotope.

• The probability of radioactive transformation depends primarily on two factors:

‐ Nuclear stability as related to the ‐to‐ ratio.

‐ The ‐ relationship among the parent nucleus, daughter nucleus and the emitted particles.

36 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity

The Origin of Nuclear Radiation and a Few Related Concepts

• Nuclear and Coulomb barrier. • Nuclear and nuclear stability. • Nucleartransformationasawaytoachievegreaternuclear stability and associated energy release.

37 NPRE 441, Principles of Radiation Protection Nuclear

Within the incredibly small nuclear size （～10‐15m）,thetwostrongest forces in , Coulomb force and strong , are pitted against each other. When the balance is broken, the resultant radioactivity yields particles of enormous energy.

Coulomb potenital

1 q1  q2 VC  , where 0 is the electrical permitivity http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 40 r 38 NPRE 441, Principles of Radiation Protection of Nucleus

• are bounded together in nucleus by the strong force, which has a short range of ~10‐15m. • The strong force is powerful enough to overcome the Coulomb repulsion between the positively charged . Coulomb potenital

1 q1  q2 VC  , where 0 is the electrical permitivity 40 r

39 NPRE 441, Principles of Radiation Protection Coulomb Barrier

40 NPRE 441, Principles of Radiation Protection Coulomb Barrier

We can use the following equation to estimate the radiuses of the Cl nucleus and the proton, R  1.3A1/3 1015 m

With A=1 and A=35 for the proton and the Cl nucleus, we have

1 q  q  1 2 , V C 40 r

where 0 is the electrical permitivity 41 NPRE 441, Principles of Radiation Protection A Simple

For example, thermal by nucleus.

42 NPRE 441, Principles of Radiation Protection Mass Defect and

In this case, the energy transition due to the mass defect is

43 NPRE 441, Principles of Radiation Protection Nuclear Binding Energy

The nuclear binding energy

In this case, the binding energy for the nucleus is given by

44 NPRE 441, Principles of Radiation Protection Nuclear Binding Energy

• Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual of the protons and which constitute it. • This difference is a measure of the nuclear binding energy, which holds the nucleus together. The binding energy can be calculated from the Einstein relationship: Nuclear binding energy = Δmc2

The nuclear binding energy

45 Nuclear Binding Energy

• Binding energy is always positive. • The average binding energy per peaks for A = 40 to 120, with a maximum of ~8.5MeV. • It then drops off for either higher or lower A. • There are a few nuclei, 4He, 12C and 16Oatthelowermass number end that have binding (per nucleon) well above that for adjacent nuclei. • In fact, these nuclei are all “multiples” of the . •And…

46 NPRE 441, Principles of Radiation Protection Fission Reactions

• A fission reaction splits up a large nucleus into smaller pieces. • A fission reaction typically happens when a neutron hits a nucleus with enough energy to make the nucleus unstable.

47 NPRE 441, Principles of Radiation Protection Average Binding Energy Per Nucleon Comparing Fusion and Fission Reactions

http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 48 NPRE 441, Principles of Radiation Protection Binding Energy of

http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html 49 NPRE 441, Principles of Radiation Protection Z Chart of the (177, 117) The nuclides are the possible nuclei of atoms. Z determines the chemistry, because the neutral with the nuclide as its nucleus has Zelectrons. Half‐life

N Source: http://www.nndc.bnl.gov/chart/reZoom.jsp?newZoom=5 50 Chart of the Nuclides

Be11 β- 11.5, 9.4 γ 2.1

51 Nuclear Stability and the Origin of Radioactivity

Secondary , e.g., gamma‐rays, X‐ rays, alpha‐particles, and

Alpha decay

Parent (Z, N)  Daughter (Z‐2, N‐2) 210 206 4 84 Po 82 Pb 2 He

Beta decay: Parent (Z, N)  Daughter (Z+1, N‐1) 𝑋 →𝑋𝑒 𝜐̅

Parent (Z, N)  Daughter (Z‐1, N+1) decay: 𝑋 →𝑋𝑒 𝜐 capture: A  A Z X  e  Z 1Y 

22 22 0 11 Na10 Ne1 

52 Chapter 1: Radioactivity Take‐Home Points Covered in Today’s Lecture

Introduction • Major sources of radiation dose to the general population a. Medical dose b. Dose from radioactive background (ranked by importance) i. Internal ingestion of radioactivity ii. Space and cosmogenic radiation iii. Terrestrial naturally occurring radioactive materials (NORM) c. Radiation dose from indoor i. Inhaled radioactive Rn form the (Rn‐222), (Rn‐220), and series (Rn219) ii. Alpha particles emitted by Rn‐222 and its daughters

Chapter 1: Radioactivity • Nuclear binding energy a. What is nuclear binding energy? b. Calculation of binding energy for given • Understanding the Chart of Nuclides a. Stable and non‐stable nuclides b. Energy release from 53 Chapter 1: Radioactivity

Alpha Decay

Key concepts • Coulomb barrier and energy release through alpha decay. • Energy spectrum of alpha particles. • Major health hazards related to alpha emission

54 NPRE 441, Principles of Radiation Protection Average Binding Energy Per Nucleon

55 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Emission

• An alpha particle is a highly energetic nucleus consisting of two neutrons and 2 protons.

• It is normally emitted from isotopes when the neutron‐ to‐proton ratio is too low – called the alpha decay.

• and atomic are conserved in alpha decays

56 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Decay –An Example

•Half‐life: 138.376 days; Decay mode: alpha‐decay (branching ratio: 100%); Energy release: 5.407MeV • 210Po has a neutron‐to‐proton ratio of 126 to 84 (1.5:1) and 206Pb has a neutron‐to‐proton ratio of 124 to 82 (~1.51:1) increased neutron‐to‐ proton ratio. • Alpha decay is also accompanied by the loss of two orbital electrons.

57 NPRE 441, Principles of Radiation Protection Nuclear Stability and the Origin of Radioactivity

Secondary radiations, e.g., gamma‐rays, X‐ rays, alpha‐particles, and electrons

Alpha decay

Parent (Z, N)  Daughter (Z‐2, N‐2) 210 206 4 84 Po 82 Pb 2 He

Beta decay: Parent (Z, N)  Daughter (Z+1, N‐1) 𝑋 →𝑋𝑒 𝜐̅

Parent (Z, N)  Daughter (Z‐1, N+1) Positron decay: 𝑋 →𝑋𝑒 𝜐 : A  A Z X  e  Z 1Y 

22 22 0 11 Na10 Ne1 

58 Nuclear Binding Energy

The nuclear binding energy

In this case, the binding energy for the deuterium nucleus is given by

59 NPRE 441, Principles of Radiation Protection Potential Energy of Nucleus

• Nucleons are bounded together in nucleus by the strong force, which has a short range of ~10‐15m. • The strong force is powerful enough to overcome the Coulomb repulsion between the positively charged protons. Coulomb potenital

1 q1  q2 VC  , where 0 is the electrical permitivity 40 r

60 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Emission

In heavy elements, It would require a minimum of ~3.8MeV for the alpha particle to “tunneling through” the potential well …

61 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Alpha Decay

With only a few exceptions (‐147), naturally occurring alpha decay are found only among elements of atomic number greater than 82 because of the following reasons: • Electrostatic repulsive force in heavy nuclei increases much more rapidly with the increasing atomic number than the cohesive nuclear force. The magnitude of the electrostatic repulsive force may closely approach or even exceed that of the nuclear force.

• Emitted alpha particles must have sufficiently high kinetic energy to overcome the potential barrier resultant from the strong nuclear force.

62 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Release from Alpha Decay

An example: Alpha decay of 226Ra

The energy release can be found using the data shown in the table previously used for deriving binding energy

63 NPRE 441, Principles of Radiation Protection Understanding the Mass Defect and Nuclear Binding Energy

64 Chapter 1: Radioactivity Energy Release in Alpha Emission A more accurate version

The required kinetic energy has to come from the decrease in mass following the decay process. The relationship between mass and energy associated with an alpha emission is given as

65 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Release from Alpha Decay

An example: Alpha decay of 226Ra

The same example, when considering the daughter atom to have two less electrons,

Note:

Md, Md: masses of the parent and daughter atoms

What is the energy of the alpha particle? 66 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Energy Spectra of Alpha Particles

m is the mass of the alpha particle, and M is the mass of the recoil nucleus.

Measured energy spectrum of alpha particles emitted from the decay of 238Pu.

NPRE 441, Principles of Radiation Protection 67 Chapter 1: Radioactivity Energy Spectra of Alpha Particles

Alpha decays are sometimes accompanied by the excited daughter products which complicates the resultant alpha particle spectra.

The kinetic energy of alpha particles is given by

E  Q A  4 / A, where A is the number of the parent nucleus and Q is the energy release.

Measured energy spectrum of alpha particles emitted from the decay of 238Pu.

68 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity Half‐Life of Alpha Emitters

The most energetic alpha particles are found to come from having relatively short half‐lives.

An early empirical rule known as the Geiger‐Nuttall law implies that

 lnT  a  bln R where T and R are the half - life of an alpha emitter and the range of the particles emitted. a and b are constants.

69 NPRE 441, Principles of Radiation Protection Chapter 1: Radioactivity A Few Remarks

• Q value has to be positive for alpha decay.

• Energy of the alpha particles generally increases with the atomic number of the parent. For example, 1.8 MeV for 144Nd to 11.6 MeV for 212mPo.

• All nuclei with mass numbers greater than A of 150 are thermodynamically unstable against alpha emission (Q is positive). However, alpha emission is a dominant decay process only for heaviest nuclei, A≥210.

70 NPRE 441, Principles of Radiation Protection