Chapter 1: Radioactivity

Chapter 1: Radioactivity

NPRE 441, Principles of Radiation Protection


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Radioactivity


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

• Radioactivity and radioactive properties of nuclide are determined bynuclear considerations and independent of chemical and physical states ofthe radioisotope.

• The probability of radioactive transformation depends primarily on twofactors:

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

‐ The mass‐energy relationship among the parent nucleus, daughternucleus and the emitted particles.


36

The Origin of Nuclear Radiationand a Few Related Concepts



• Nuclear force and Coulomb barrier.• Nuclear binding energy and nuclear stability.• Nuclear transformation as a way to achieve greater nuclear

stability and associated energy release.

37

Nuclear Forces


Within the incredibly small nuclear size （～10‐15m）, the two strongestforces in nature, Coulomb force and strong nuclear force, are pitted againsteach other. When the balance is broken, the resultant radioactivity yieldsparticles of enormous energy.

http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html

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Coulomb potenital

VC 1

40

q1 q2

r, where 0 is the electrical permitivity

Potential Energy of Nucleus


• Nucleons are bounded together in nucleus by the strong force, which has a shortrange of ~10‐15m.

• The strong force is powerful enough to overcome the Coulomb repulsion betweenthe positively charged protons.

Coulomb potenital

VC 1

40

q1 q2


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Coulomb Barrier

NPRE 441, Principles of Radiation Protection40

Coulomb Barrier


We can use the following equation to estimate the radiuses of the Cl nucleus and theproton,

mAR 153/1 103.1

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

CV 140

q1 q2

r,

where 0 is the electrical permitivity41


A Simple Nuclear Reaction

For example, thermal neutron captureby hydrogen nucleus.

42

Mass Defect and Nuclear Binding Energy


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

43

Nuclear Binding Energy


The nuclear binding energy

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

44


• Nuclei are made up of protons and neutron, but the mass of anucleus is always less than the sum of the individual masses ofthe protons and neutrons which constitute it.

• This difference is a measure of the nuclear binding energy, whichholds the nucleus together. The binding energy can be calculatedfrom the Einstein relationship:

Nuclear binding energy = Δmc2

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• Binding energy is always positive.

• The average binding energy per nucleon 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 16O at the lower massnumber end that have binding energies (per nucleon) well abovethat for adjacent nuclei.

• In fact, these nuclei are all “multiples” of the alpha particle.

• And …

46

Fission Reactions

• A fission reaction splits up alarge nucleus into smallerpieces.

• A fission reaction typicallyhappens when a neutron hits anucleus with enough energy tomake the nucleus unstable.


Average Binding Energy Per Nucleon Comparing Fusion and Fission Reactions


http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html48

Binding Energy of Atoms


http://230nsc1.phy‐astr.gsu.edu/hbase/hframe.html49

The nuclides are the possible nuclei of atoms. Z determines the chemistry, because the neutral atom with the nuclide as its nucleus has Z electrons.

(177, 117)

NSource: http://www.nndc.bnl.gov/chart/reZoom.jsp?newZoom=5

Z

Half‐life

Chart of the Nuclides

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Chart of the Nuclides

Be11β- 11.5, 9.4γ 2.1

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Nuclear Stability and the Origin of Radioactivity

Beta decay:

Parent (Z, N) Daughter (Z+1, N‐1)

Positron decay:

Electron capture:

Alpha decay

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

HePbPo 42

20682

21084

01

2210

2211 NeNa

YeX A

ZAZ 1

52

𝑋 → 𝑋 𝑒 𝜐


Parent (Z, N) Daughter (Z‐1, N+1)

Parent (Z, N) Daughter (Z‐2, N‐2)

Take‐Home Points Covered in Today’s Lecture


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Introduction• Major sources of radiation dose to the general population

a. Medical doseb. Dose from radioactive background (ranked by importance)

i. Internal ingestion of radioactivityii. Space and cosmogenic radiation iii. Terrestrial naturally occurring radioactive materials (NORM)

c. Radiation dose from indoor radon i. Inhaled radioactive Rn isotopes form the uranium (Rn‐222), thorium (Rn‐220), and actinium

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 radionuclides

• Understanding the Chart of Nuclidesa. Stable and non‐stable nuclidesb. Energy release from radioactive decay

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

Average Binding Energy Per Nucleon


Alpha Emission


• An alpha particle is a highlyenergetic helium nucleusconsisting of two neutronsand 2 protons.

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

• Atomic number and atomicmass number are conservedin alpha decays


56

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 aneutron‐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

Nuclear Stability and the Origin of Radioactivity

Beta decay:

Parent (Z, N) Daughter (Z+1, N‐1)

Positron decay:

Electron capture:

Alpha decay

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

HePbPo 42

20682

21084

01

2210

2211 NeNa

YeX A

ZAZ 1

58



Parent (Z, N) Daughter (Z‐1, N+1)

Parent (Z, N) Daughter (Z‐2, N‐2)




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

59

Potential Energy of Nucleus


• Nucleons are bounded together in nucleus by the strong force, which has a shortrange of ~10‐15m.

• The strong force is powerful enough to overcome the Coulomb repulsion betweenthe positively charged protons.

Coulomb potenital

VC 1

40

q1 q2


60

Alpha Emission



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

61

Alpha Decay


With only a few exceptions (Samarium‐147), naturally occurring alphadecay are found only among elements of atomic number greater than 82because of the following reasons:


• Electrostatic repulsive force in heavy nuclei increases much more rapidlywith the increasing atomic number than the cohesive nuclear force. Themagnitude of the electrostatic repulsive force may closely approach oreven exceed that of the nuclear force.

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

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Energy Release from Alpha Decay



An example: Alpha decay of 226Ra

The energy release can be found using the datashown in the table previously used for derivingbinding energy

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Understanding the Mass Defect and Nuclear Binding Energy

64

Energy Release in Alpha EmissionA more accurate version



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

65

Energy Release from Alpha Decay



An example: Alpha decay of 226Ra

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

66What is the energy of the alpha particle?

Note:Md,Md: masses of the parentand daughter atoms

Energy Spectra of Alpha Particles



Measured energy spectrum of alphaparticles emitted from the decay of238Pu.

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

67

Energy Spectra of Alpha Particles



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

Measured energy spectrum of alphaparticles emitted from the decay of238Pu.

E Q A 4 / A,where A is the atomic mass number of the parent nucleus and Q is the energy release.

The kinetic energy of alpha particles is givenby

68

Half‐Life of Alpha Emitters



The most energetic alpha particles are found to come from radionuclide havingrelatively short half‐lives.

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

constants. are b and a emitted. particles theof range theandemitter alphaan of life-half theare R and T where

lnln RbaT

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A Few Remarks

• Q value has to be positive for alpha decay.



• Energy of the alpha particles generally increases with the atomic numberof 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 arethermodynamically unstable against alpha emission (Q is positive).However, alpha emission is a dominant decay process only for heaviestnuclei, A≥210.

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Chapter 1: Radioactivity

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