basic physics and radiation · 2019-05-16 · basic physics and radiation safety in nuclear...

Basic Physics and RadiationSafety in Nuclear Medicine

G.S. Pant, Ph.D, FICNM

Retd.-Professor (Medical Physics)Department of Nuclear Medicine,

All India Institute of Medical Sciences,New Delhi - 110 029 (India)

&Ex. Consultant Medical Physicist and Head,

Cyclotron, Medical Imaging Department,King Fahad Specialist Hospital,

Dammam, Kingdom of Saudi Arabia.

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PREFACEMedical Physics and Radiation Safety are integral parts of radiation oncology,

radiology and nuclear medicine in any medical institution or hospital. Remarkabledevelopment has taken place in these disciplines of medicine particularly due to thephenomenal progress in electronics and computing. I have witnessed the technologicaldevelopments in these three disciplines during my professional career of over 3 decades,while working at the All India Institute of Medical Sciences (AIIMS), New Delhi.Technology has enabled us to use both ionizing and non-ionizing radiations for medicalimaging with extremely good image quality, which in turn helps the physicians inmaking proper diagnostic interpretation. In nuclear medicine there has also beentremendous progress in the production of newer radioisotopes and radiopharmaceuticalsfor diagnostic and therapeutic applications. While, the use of ionizing radiation fordiagnosis and/or therapy has been increasing with great enthusiasm, adequate safetymeasures against the possible radiation hazards have become all the more important thanever before. Fortunately, they are realized and also have been given due consideration inthe current clinical practice of these disciplines. Proper radiation safety standards areabsolutely necessary in any facility, using ionizing radiation, to ensure the safety ofoccupational staff, patients and the general public from radiation hazards. World over,each country has its own regulatory body to monitor the radiation safety standards in afacility, using ionizing radiation, so that the staff, patients and public at large do notreceive radiation exposure beyond the prescribed limits set by the regulatory orcompetent body.

The basic science of nuclear medicine is an essential component of clinical nuclearmedicine, which covers all the relevant topics in basic physics, imaging techniques,radiation dosimetry, radiation safety in nuclear medicine etc. In view of the fact thattherapeutic nuclear medicine has been progressing with good pace, internal dosimetryneeds to be given adequate space. In this second edition of the book few more chaptershave been added in dosimetry and PET/MRI with its clinical applications.

This edition consists of 41 chapters, divided into six parts. The first part, consists of12 chapters, devoted to the introductory physics, radioactivity, interaction of radiation,counting statistics, radiation detectors, radiation detection in vitro and in vivo, planar andSPECT imaging in nuclear medicine with QC procedures for imaging instrumentation,image filtering, image quality and introduction to Fourier transform.

The second part, with six chapters, is devoted to internal dosimetry. It includes thebasic (medical internal radiation dose) MIRD schema and its application with examplesfor better understanding of the readers, dosimetry in radioiodine therapy, dosimetry inLutetium targeted therapy, dosimetry in radioembolisation in hepatocellular carcinoma(HCC) and application of Olinda/EXM software in estimating organ, and whole bodydose (WBD) in diagnostic nuclear medicine procedures. Internal dosimetry involvescomplex equations and measurements for some of the parameters for organ/WB doseestimation. There are small centers of nuclear medicine, where radioiodine therapy ispracticed, but resources may not be available for the measurement of some parameters as

required for dose calculation. Experienced nuclear medicine physician’s comments inradioiodine therapy as given in this edition may be useful for them.

There are four chapters, in the third part where, the physical characteristics ofradionuclides are given by eminent scientists. This part also covers radiopharmaceuticalsfor conventional nuclear medicine (planar and SPECT imaging) and for positronemission tomography (PET). It also includes PET radiochemistry andradiopharmaceutical QC procedures. For the benefit of readers, a chapter on clinicalapplications of these radionuclides and radiopharmaceuticals in clinical nuclear medicine,both for diagnosis and therapeutics is also added.

The fourth part, with 11 chapters, covers cyclotron, PET/CT, PET/MR imaging.The basic principle and operation of a medical cyclotron, physics of PET, technicalaspects of PET/CT and image registration. Clinical applications of PET/CT andPET/MRI have been written by nuclear medicine physicians with vast experience inthese disciplines. Use of PET/CT in radiotherapy treatment planning is written by aneminent medical physicist. Chapters on basics of CT and MR imaging, as relevant tonuclear medicine, have also been included for the benefit of readers.

The fifth part (with 3 chapters), includes some of the quantification techniques innuclear medicine; such as, background subtraction (particularly in renography),deconvolution analysis for estimating renal transit time parameters and tracer kinetics.

Finally the sixth part, with five chapters, focuses on radiobiology and health physics.It includes, radiobiological concepts, radiobiological basis of radiological protection,ICRP recommendation, radiation safety in nuclear medicine, and diagnostic referencelevels in nuclear medicine.

I feel that, the book with good scientific content as mentioned above should beuseful to the students in nuclear medicine and allied sciences.

Manuscripts, as received from the authors have been edited to the extent considerednecessary for readers. However, the illustrations/figures, references used and viewsexpressed/implied remain the responsibility of authors.

G.S. Pant

ACKNOWLEDGEMENTSThe authors and co-authors of most of the chapters have revised their earlier

manuscripts published in the first edition of this book. Some of them have writtenadditional chapters on dosimetry and PET/MRI. All these authors, experts in theirrespective fields, have been very kind to provide their manuscript well in time. BothIndian and overseas authors have squeezed considerable time out of their very busyschedules and commitments either for writing a new chapter or revising their earlierchapters. I sincerely express my thanks and gratitude to all the authors in this bookand gratefully acknowledge their contributions.

The valuable suggestions made by faculty and students in nuclear medicine atAIIMS, where I worked for about 36 years were also of great help in giving propershape to this book. The idea of bringing out second edition of the book came onlyafter, I received appreciations and suggestions from some of the readers, from severalparts of the country. In fact, the chapter on PET/MRI has been added on theirsuggestion. I am confident that, the efforts of authors will be enjoyed and valued bythe readers.

Help rendered by my friends and students in editing some of the chapters isthankfully acknowledged.

Lastly, I am thankful to the Himalaya Publishing House Pvt. Ltd., Mumbai fortheir full cooperation and support in bringing out this edition.

G.S. Pant

CONTENTSPart - I

Basic Physics and Imaging Techniques

Page No.

1. Basic Atomic and Nuclear Physics 3G.S. Pant and H. Rajabi

2. Interaction of Radiation with Matter 14G.S. Pant

3. Radioactivity 25G.S. Pant and A.K. Pandey

4. Counting Statistics 40A.K. Pandey

5. Radiation Detectors 67G.S. Pant

6. Radionuclide Dose Calibrator 81G.S. Pant

7. Scintillation Detection (in vitro) 87G.S. Pant

8. Radiation Detection in vivo and Gamma Camera Imaging 93G.S. Pant

9. Single Photon Emission Tomography (SPECT) 122G.S. Pant and H. Rajabi

10. Image Filtering in Nuclear Medicine 152H. Rajabi and A.K. Pandey

11. Image Quality in Nuclear Medicine 164G.S. Pant

12. Fourier Transform: Basic Concepts 169H. Rajabi

Part - II

Dosimetry13. Dosimetry of Internally Administered Radionuclides 189

A.R. Reddy

14. Radiation Dosimetry in Graves’ Disease 212G.S. Pant

15. Dosimetry with Iodine-131 in Differentiated Thyroid Cancer 218Praveen Kumar and C.S. Bal

16. Dosimetric Considerations in Lutetium based Targeted Radionuclide Therapy 236Ishita B. Sen and Parul Thakral

17. Dosimetric Aspects in Radioembolisation with 90Y Microspheres and188Re-HDD-Lipiodol for Hepatocellular Carcinoma (HCC) 250G.S. Pant and Ajay Kumar

18. Dose Estimation in Diagnostic Nuclear Medicine Proceduresusing OLINDA/EXM Personal Computer Code 255Aruna Kaushik

Part - III

Radionuclides and Radiopharmaceuticals in Nuclear Medicine19. Radionuclides in Medicine and Research 269

N. Ramamoorthy and Meera Venkatesh

20. Radiopharmaceuticals in Clinical Nuclear Medicine 288M.G.R. Rajan

21. PET Radiochemistry and PET Radiopharmaceuticals 304M.G.R. Rajan

22. Applications of Radionuclides in Clinical Nuclear Medicine 331Girish K. Parida, Chetan D. Patel and C.S. Bal

Part - IV

Cyclotron, PET/CT and PET/MR23. Medical Cyclotron: Basic Principle and Operation 349

G.S. Pant and S. Senthamizhchelvan

24. PET/CT: Physical Principles, Instrumentation and Performance Evaluation 362G.S. Pant

25. Combined PET/CT: Technical Aspects and Image Registration 391Habib Zaidi

26. Image Correction Techniques in SPECT and PET 399Habib Zaidi

27. Computed Tomography in PET/CT 409Mahadevappa Mahesh, Devasenathipathy Kandasamy and Raju Sharma

28. Clinical Applications of PET and PET-CT 422Girish K. Parida and Rakesh Kumar

29. PET Imaging: Potential Applications in Gene and Stem Cell Therapy 448Tarun Singhal

30. PET-CT Based Radiotherapy Treatment Planning 455T. Ganesh, S. Agrawal and R. Prabhakar

31 MR Imaging – Basic Concepts 469S. Senthil Kumaran

32. Basic Introduction to PET/MRI 487S. Senthamizhchelvan and G.S Pant

33. Clinical Applications of PET/MRI 495Amarnath Jena

Part - V

Quantification Techniques in Nuclear Medicine34. Background Subtraction in Nuclear Medicine 509

H. Rajabi and G.S. Pant

35. Deconvolution Analysis and Renal Transit Time Parameters 518H. Rajabi and G.S. Pant

36. Radiotracer Kinetics: Applications in Nuclear Medicine 532Bharathi D. Jagadeesan

Part - VI

Health Physics and Radiation Safety37. Basics of Radiobiology 549

G.S. Pant

38. Radiobiological Basis of Radiation Protection 566B.S. Rao

39. ICRP Recommendations 579A.R. Reddy and S.C. Jain

40. Radiation Safety in Nuclear Medicine 600G.S. Pant and B. Rajashekhar Rao

41. Diagnostic Reference Levels for Nuclear Medicine 656S.C. Jain and A.R. Reddy

Annexures 667

Index 671

CONTRIBUTORS

Shaleen Agrawal, MDConsultant Radiation OncologistFortis Memorial Research InstituteSector 44, Gurugram, Haryana (India)[email protected]

C.S. Bal, MD, FICNMProfessor & HeadDept. of Nuclear Medicine and PETAIIMS, New Delhi-110029 (India)[email protected]

Bharathi D. Jagadeesan, MDAssociate Professor, University of MinnesotaRadiology, Neurology and NeurosurgeryMMC 292, Mayo Memorial Building,420 Delaware St SE,Minneapolis, MN 55455 (USA)[email protected]

T. Ganesh, Ph.D., DABRChief Medical PhysicistDept. of Radiation OncologyManipal hospital,Dwarka, New Delhi (India)[email protected]

S.C. Jain, Ph.D.6312 Jain Mandir Street,Gandhi Nagar, Delhi (India)[email protected]

Amarnath Jena, MDSenior Consultant (Nuclear Medicine)PET SUITE, Department of Molecular Imaging and Nuclear MedicineIndraprastha Apollo Hospital, New Delhi (India)[email protected]

D. Kandasamy MD, DNB, FRCRAssociate Professor,Department of Radiology,All India Institute of Medical Sciences, New Delhi, (India)[email protected]

Aruna Kaushik, Dip.R.P, Ph.D.Scientist and RSOInstitute of Nuclear Medicine & Allied SciencesMIRC, Brig. S.K. Mazumdar Marg, Timarpur,Delhi (India)[email protected]

Ajay Kumar, MD, Ph.D., DNB, MNAMSAssistant ProfessorDept. of Pediatrics, Neurology and RadiologyPET Center, Children’s Hospital of Michigan, Detroit Medical Center3901 Beaubien Street, Detroit, MI 48201 (USA)[email protected]

Rakesh Kumar, MD, Ph.D., FICNM, FAMSProfessor and Head Diagnostic Nuclear MedicineDept. of Nuclear MedicineAIIMS, New Delhi – 110029 (India)[email protected]

S. Senthil Kumaran, Ph.D.ProfessorDept. of NMR,AIIMS, New Delhi (India)[email protected]

Mahadevappa Mahesh, MS, Ph.D., FAAPM, FACR, FACMP, FSCCTProfessor - The Russell H. Medicine Department of Radiology and Radiological ScienceProfessor of Medicine - CardiologyAssociated Faculty - Armstrong Institute for Patient Safety and QualityJohns Hopkins University School of MedicineChief Physicist - Johns Hopkins HospitalJoint Appointment - Johns Hopkins Bloomberg School of Public Health (USA)[email protected]

A.K. Pandey, Ph.D.Associate Professor (Medical Physics)Department of Nuclear Medicine,AIIMS, New Delhi-110029 (India)[email protected]

G.S. Pant, Ph.D., FICNMRetd.-Professor (Med Phys)Dept. of Nuclear MedicineAIIMS, New Delhi (India)&Ex-Consultant Medical Physicist andHead Cyclotron,KFSH, Dammam, [email protected]

Girish K. Parida, MDSenior Resident,Dept. of Nuclear MedicineAIIMS, New Delhi-110029 (India)[email protected]

Chetan D. Patel, MDProfessor (Nuclear Medicine)Dept. of Nuclear MedicineAIIMS, New Delhi-110029 (India)[email protected]

R. Prabhakar, Ph.D.Lead Physicist, PeterMac Cancer Centre(Moorabbin) Adjunct Associate Professor at RMITand Manash University, [email protected]

Hossein Rajabi, Ph.D.Associate professorDepartment of Medical PhysicsSchool of Medical SciencesTarbiat Modares UniversityTehran (Iran)[email protected]

M.G. Ramakrishna RajanRaja Ramanna Fellow, Dept. of Atomic Energy,Ex Outstanding Scientist and Head, Radiation Medicine Centre,Bhabha Atomic Research Centre, Mumbai (India)[email protected]

B. Rajashekharrao, Ph.D.Former Sr. Scientific Officer and Officer-in-Charge,Radiation Hazard Control Unit, Radiation Safety Systems Division,Radiation Medicine Centre, Bhabha Atomic Research Centre, Mumbai (India)[email protected]

Natesh Ramamoorthy, Ph.D.Adjunct Faculty, National Institute of Advanced Studies (NIAS), BangaloreEx-Director, Div of Physical and Chemical Sciences, IAEA, Vienna;Ex-Chief Executive, Board of Radiation and Isotope Technology, andEx-Associate Director, Isotope Group, BARC, Mumbai (India)[email protected]

B.S. Rao, Ph.D.Ex-Head, RPAD, BARC33A/31 Manish Nagar,J. P. Road, Andheri WestMumbai (India)[email protected]

A.R. Reddy, Ph.D.Ex-Director (DRDO)Hyderabad (India)[email protected]

Raju Sharma, MD, MAMS, FICRProfessorDepartment of RadiologyAll India Institute of Medical SciencesNew Delhi (India)[email protected]

Ishita B. Sen, MDDirector, Department of Nuclear Medicine and PETFortis Memorial Research Institute, Gurgaon, Haryana (India)[email protected]

S. Senthamizhchelvan, Ph.D., DABR, DABSNMDirector, Radiation Oncology & Lead Medical Physicist,CHI-Memorial Hospital,Chattanooga, TN 37404 (USA)[email protected]

Parul Thakral, Ph.D.Research Officer,Department of Nuclear MedicineFortis Memorial Research Institute, Gurgaon, Haryana (India)[email protected]

Tarun Singhal, MDAssistant Professor of Neurology, Harvard Medical SchoolAssociate Neurologist, Brigham and Women’s HospitalBuilding for Transformative Medicine60 Fenwood Road, Boston, MA 02115 (USA)[email protected]

Meera Venkatesh, Ph.D.Director, Division of Physical and Chemical SciencesDepartment of Nuclear Sciences and Applications,International Atomic Energy Agency (IAEA)Wagramer Strasse 5A-1400, Vienna, (Austria)&Head, Radiopharmaceutical Division, BARC& Senior General Manager, BRITBARC, Mumbai- (India)[email protected]

Habib Zaidi, Ph.D.Head of PET Instrumentation &Neuroimaging Laboratory (PIN Lab)Geneva University HospitalDivision of Nuclear MedicineCH-1211 Geneva (Switzerland)[email protected]

Basic Physics andImaging Techniques

Part - I

2 Basic Physics and Radiation Safety in Nuclear Medicine

3Basic Atomic and Nuclear Physics


G.S. Pant and H. Rajabi

Atomic radiations find many peaceful and beneficial applications particularly in the field ofmedical diagnosis and treatment. Their safe use needs knowledge of the basics of atomic andnuclear physics, which is briefly described in this chapter.

Atom

An atom is the smallest unit of a chemical element that possesses the properties of that element.Atoms rarely exist alone, often combine with other atoms to form a molecule, which is thesmallest component of a chemical compound.

In his atomic theory, John Dalton (1808) described that elements consisted of tiny particlescalled atoms and that all the atoms of an element are exactly identical. The elements are differentdue to the size and weight of their atoms. Almost at the same time Dmitri Mendeleev andJ.L. Meyer arranged atoms of different elements in order of their atomic weight in a table(periodic table) such that elements with similar chemical properties fell into the same column.

Discovery of electron by J.J. Thomson (1897) was the beginning of modern atomic theory.The discovery of X-rays by Roentgen in 1895 and radioactivity by Becquerel in 1896, attracted theattention of physicists to conduct lots of experiment to reveal the atomic structure. During 1908 to1913, Hans Geiger and Ernest Marsden performed a landmark series of experiments on scatteringof alpha particle over a thin layer of gold. Their experiments showed that many of alpha particlesare scattered in large angles, which could not be explained by Thomson model of atom.

Rutherford (1910) concluded from Geiger-Marsden experiments, that atom has a compactpositively charged mass surrounded by a cloud of negatively charged electrons. This smallmassive positively charged object was called the nucleus. Thereafter, scientists proposed theplanetary model of the atom. The electrons were held in orbits around the nucleus due to balancebetween the attractive electric and outward centrifugal forces. This model became totallyinconsistent with Maxwell’s electromagnetic theory. According to classical physics, anaccelerated charged particle emits electromagnetic radiation. An electron in an orbit around anucleus should continuously emit electromagnetic radiation and lose its kinetic energy. Theelectron should therefore, spiral into nucleus within a short time. Thus, classical physics failed toexplain the modern atomic model.


The German physicist, Max Planck, solved the problem using a mathematical trick! Hispostulation (trick) was the birth of quantum physics, that honored him with the Nobel Prize in1918. Planck assumed the vibrating atoms and molecules are confined to a set of equally-spacedfrequencies. In this way, the predicted spectra perfectly matched the experimentally determinedspectra. Based upon the relationship between the frequency of an oscillator and its energy, theenergy levels of an atomic oscillator is not continuous, but has certain discrete values,corresponding to the frequency they oscillate with. Later on the quantization was extended toother physical concepts such as momentum and magnetic dipole moments.

Based on the Planck’s postulation, Bohr, in 1913, proposed his quantized shell model of theatom to explain why electrons are stable in their orbitals around the nucleus. He proposed that theelectrons move in discrete orbits of fixed size and energy. Energy can be emitted only when theelectron jumps from one orbit to another, but not when it is in an orbit. An atom is stable when allthe electrons are in the smallest possible orbit. Electrons could jump from one orbit to anotheronly by emitting or absorbing energy in fixed quanta. Bohr, also postulated that the angularmomentum of the electron is quantized. Bohr’s atomic theory was mainly based on the Planck’spostulation (1900), that energy can only be emitted or absorbed in discrete amounts, which hecalled quanta. Using Planck’s constant, Bohr, obtained an accurate formula for the energy levelsof the hydrogen atom. Although he failed to explain the energy levels of atoms, other thanhydrogen (complicated than hydrogen), his model was important, as it introduced, the concept ofthe quantized orbital.

Ernest Rutherford in 1920, used the word proton (first in Greek) for hydrogen nucleus. Healso postulated, that another kind of particle must be present in the nucleus of atoms. Hispostulation was based on high repulsive force between positively charged protons in the nucleus.He assumed that an electrically neutral particle is needed to neutralize the repulsive force betweenprotons. In 1932 James Chadwick, discovered the neutron and measured its mass.

The modern atomic model is rather complicated and developed, based on the modernquantum mechanics. Erwin Schrodinger and Wiener Heisenberg, independently developed, thisnew comprehensive theory of waive particle duality (1925). They unified the wave-particleduality into a single consistent theory. The theory could explain many of the natural phenomenasuccessfully, and was accepted by all physicists. We have to remember that for a totally freeelectron nothing is quantized. A free electron can have a continuous range of energy andmomentum. But, when it is bound to an atom, its energy and angular momentum becomesquantized.

Wave-Particle DualityClassical physics assumes that particles are particles and waves are waves, they cannot be both.Einstein (1905) while explaining the photoelectric effect postulated that electromagnetic radiationhas wave-particle nature. He used the term photon to refer the particle of electromagneticradiation. He proposed an extraordinary simple formula to relate the energy of the photon to thefrequency and wavelength of electromagnetic wave.

chhvE ... (1)


In this equation h is the Planck’s constant (6.634 × 10–34 Js), and c is the velocity of light invacuum.

De Broglie generalized the idea, and postulated that all sub atomic particles have wave-particle nature. In some phenomenon the particle behaves as a particle and in some phenomenonit behaves as a wave. In no phenomena both wave and particle nature is simultaneously observed.This is called the wave-particle duality of nature. He suggested a simple equation that relatesfundamental characteristics of particles and waves. Particles have momentum p, waves havewavelengths and the two are related by the equation:

p

h ... (2)

The wave-particle duality can only be appreciated in microscopic scale. Assume a ball ofmass 0.1 kg is thrown with a velocity of 10 m/s. The associated wavelength is approximately6.6 × 10–33 m that is infinitesimal compared to the size of the ball. Even if such a ball moves withthe velocity of light (c = 3 × 108 m/sec) the wave nature is not appreciable. Only in the case ofparticles with a very small mass (such as sub atomic particles) the associated wave is appreciable.Electron microscope is an instrument that proves the accuracy of the wave-particle duality. Inmacroscopic scale De Broglie theory is gobbledygook. Electrons around an atom have wave-particle duality; with each electron a wave is associated.

Uncertainty PrincipleClassical physics assumes that measuring the precise location and velocity of objects is alwayspossible. Heisenberg, however, discovered that this is not true at the atomic level. He stated thatthe act of observation interferes with the location and velocity of very small particles such aselectrons. Observation requires light, which has momentum. When a photon of light interacts withan electron, momentum is exchanged between two particles. The result is change in both locationand velocity of the electron. In general, the act of measurement distorts the location, andmomentum of particles due to the wave-particle duality, and unavoidable interaction between theobject (to be observed) and observing instrument. However, the uncertainty in measurement ofposition and momentum, does not arise, due to imperfect instrumentation.

In a light microscope, objects can be seen to accuracy at best of about the wavelength of theradiation being used. The shorter the wavelength, the more accurate is the positioning. But shorterwavelength corresponds to higher frequency and higher energy (Eq. 1.). Therefore moremomentum is transferred to object, when photon strikes the object. It means that increasing theaccuracy in positioning, corresponds to increased error in the measurement of momentum andvice versa. Thus, it is impossible to measure both the exact position, and the exact momentum ofa particle simultaneously.

If using the light of wavelength the position can be measured at best to an accuracy ofabout X /2

The corresponding momentum of such photon can be determined by = h/p Therefore, theuncertainty in measuring object momentum could be up to p h/ The product of theseuncertainties is given by:


2.

hpx

The uncertainty could be worse than this if more than one photon is required formeasurement. The more careful calculation reveals that

2.

hpx ... (3)

This is the mathematical expression of Heisenberg’s uncertainty principle. In macroscopiclevel, such uncertainty makes no sense. However, it has important implications in measurementsat the atomic level.

Schrodinger Equation

Erwin Schrodinger, put the ideas developed by de Broglie, Heisenberg, Planck and Bohr together,and made an equation, that is named after him as Schrodinger equation. In classical physics, thereare equations, that can be used to describe a wide variety of waveforms. Schrodinger, amathematical physicist, found an alternative definitive equation; whose solutions would describethe De Broglie wave regardless of the circumstances. This equation can in principle predict theproperties, and reactivity of all atoms and molecules.

Schrodinger assumed, that any particle may be represented by a complex wave function ofposition and time, (x, y, z, t)The associated waves are used to describe the particles’ properties.The main attributes of waves functions are:

Generally, but not necessarily, they are complex functions.

They are single-valued, and continuous functions of x, y, z and t.

They possess the whole physical information of the particle.

They cannot be measured with any physical instrument.In the most general form Schrodinger equation can be written as:

H = E ... (4)

Where E is the energy of the particle, and H is a quantum mechanical operator; amathematical operator, that describes the system under investigation. Part of the development ofquantum mechanics is the application of the operators, associated with the parameters thatdescribe the system. The Operator associated with the kinetic and potential energies for a particlein one dimension is:

)(8 2

2

2

2

xVxm

hHoperator

... (5)

Applying this operator on the wave function implies

0)(8 2

2

2

2

UExm

h... (6)

This is the Schrodinger equation in its simplest form. In this equation ‘m’ and ‘U’, are themass and potential energy of the particle respectively. The solution of the Schrodinger equation


even for the simplest atom, hydrogen is a formidable mathematical problem, which is beyond thescope of this book.

Electron ConfigurationElectrons around a nucleus can be described with wave functions. Wave functions determine thelocation, energy and momentum of the particle. The square of a wave function gives probabilitydistribution of the particle. At a given time electron can be anywhere around the nucleus, butdifferent locations have different probabilities. The space around the nucleus in which theprobability is highest is called an orbital. This is totally different from classical concept of orbital.In quantum mechanics, orbital is a mathematical concept rather than a physical concept, andsuggests the average geometrical location of an electron. If the energy of the electron changes,this average also changes. For the single electron of hydrogen atom an infinite number of wavefunction and therefore infinite number of orbital exist.

Orbital can completely be described using the corresponding wave function, but the processis tedious and difficult. An orbital can be easily described by four quantum numbers.

The principal or shell quantum number (n) characterizes the total energy, and shell sizeof the atom. It is an integer and can have value from 1 to , but practically n is alwaysless than 8. Maximum number of electrons in orbital n, is 2n2. The shells of electronsare labeled alphabetically as K(n = 1), L(n = 2), M(n = 3), etc. based on the principalquantum number.

The orbital quantum number l relates to the angular momentum of the electron; l cantake integer values from 0 to n–1. In a stable atom its’ value does not go beyond 3.Orbital quantum number characterises the configuration of the electron orbital. In thehydrogen atom the value of l does not appreciably affect the total energy, but in atomswith more than one electron, the energy depends both on n and l. The sub-shells ororbitals of electrons are labelled as s(l = 0), p (l = 1), d(l = 2) and f(l = 3).

The azimuthal or magnetic quantum number m1 relates to the direction of the electron’sangular momentum, and takes on integer values from –l to +l.

The spin quantum number ms, relates to electron angular momentum, and can have onlytwo values

21 or

21 .

Wolfgang Pauli (1925), added a complementary rule for arrangement of electron around thenucleus. The postulation is now called Pauli’s exclusion principle, and states that; no twoelectrons can have all quantum numbers same or exist in identical quantum states.

The filling of electrons in orbitals obeys the so-called Aufbau principle, degenerate orbitalsand Hund rule. The Aufbau principle assumes that electrons are added to an atom, one at a time,starting with the lowest energy orbital, until all of the electrons have been placed in anappropriate orbital. Electrons fill degenerate orbitals (orbitals with same energy but may be withdifferent orientation) according to Hund's rule one electron is added to each of the degenerateorbitals in a subshell before second is added to any orbital in the subshell.


For example, if two electrons are to be placed into the 2p subshell, we put one electron intoeach of these orbitals first. Therefore, in carbon (Z = 6) : electron filling will be arranged as 1s2

2s2 2px1 2py1.

The sequence of energy states and electron filling in orbitals of a multi-electron atom can berepresented as:

1s – 2s – 2p – 3s – 3p – 4s – 3d – 4p – 5s – 4d – 5p – 6s – 4f – 5d – 6p – 7s - 5f – 6d – 7pThe electron filling sequence can also be shown diagrammatically (Fig. 1).

Fig. 1: Diagrammatic representation of electron filling in orbits

Table 1: Electron configuration of atoms with low Z

Atom Atomic number Electron configuration

H 1 1s1 (one electron in the 1s orbital)

He 2 1s2 (two electrons in the 1s orbital)

Li 3 1s2 2s1 (two electrons in the 1s and one in 2s orbital)

Be 4 1s2 2s2 (two electrons in the 1s and two in 2s orbital)

B 5 1s2 2s2 2p1 (two electrons in the 1s, two in 2s and one in 2p orbital)

1s

2s

3s

4s

5s

6s

7s

8s

7p

6p

5p

4p

3p

2p

3d

4d

4d

6d

5f

4f


Electron Binding EnergiesA free electron is assumed to have zero potentialenergy. We have to give some energy to the boundelectrons to make them free from the atom.Therefore, we can assume that, electrons around anucleus have negative potential energy. The absolutevalue of the potential energy is called bindingenergy, the minimum energy that is required to makean electron free of the atom.

In an atom different shells have differentbinding energy. The K(n = 1) shell has the minimumpotential energy or maximum binding energy. Thebinding energy decreases (potential energyincreases) as the principle quantum numberincreases. The binding energy of the innermost shellis the highest (tightly bound), and that of theoutermost shell is the lowest (loosely bound).Binding energies and energy differences aresometimes displayed on an energy level diagram(Fig. 2). A fastidious look to the matter reveals thatno two electrons around a nucleus have exactly thesame energy levels. However the energy differencebetween the electrons in the same sub-shell isusually negligible.

Fig. 2: Energy level diagram of lead (Pb).Electron transition from higher to lowerenergy level results in the emission ofcharacteristic X-rays. For exampletransition from L to K shell will result in acharacteristic x-ray photon of 73 keV.

Atomic EmissionsTheoretically, the principal quantum number can have integer values from 1 to infinity. It meansthat, there can be infinite number of orbitals around an atom. However, in reality, atoms havefinite number of electrons; hence most of the orbitals are vacant. Stability principle requires thatelectrons to be in the minimum possible energy level or in the innermost orbitals. However,there is no restriction for an electron to move into outer orbitals, if it gains sufficient energy asrequired. If the energy level of two orbitals is close enough (up to Heisenberg uncertainty)electron can easily transfer between the two. Electrons can also transfer to vacant orbitals, if theexact required energy is supplied to them. The important point to remember is that, electronsaround an atom can exist only in orbitals, not in between. It is forbidden to have an electron withthe energy level, that does not exactly match with orbital energy. This implies that an atomicelectron can absorb or release energy that is; exactly equal to the energy difference between theoriginal and destination orbital.

If an electron absorbs external energy, that is more than or equal to the binding energy of theelectron, the electron is freed from the atom. A pair of ion, the electron and the atom with positivecharge, is created. This process is termed as ionisation. If the external energy is more than the

Binding Energy in keV0.15

0.9

3.8

15

0.75 keV0.15 keV

ON

2.9 keV

11.2 keV

73 keV

L

W

88 K


binding energy of the electron, the excess energy in divided between the two in such a way, thatconservation of momentum is preserved. The energy level of a free electron is not necessarilydiscrete.

If an electron absorbs energy, and is elevated to outer orbitals, the original orbital does notremain vacant. Soon the vacancy is filled by electron from outer layers. This is a random process,and occupier may be any electron from outer orbital. However, closer electron has more chance tooccupy the vacancy. The process may involve displacement of one or more electrons. In eachindividual filling-up process, a quantum of energy equal to the difference between the bindingenergies E2 – E1 of the two involved orbitals is released, usually in the form of a single photon.The frequency and wavelength of the emitted photon (radiation) is as follows,

chhvEEE 12 ... (7)

When an atom has excess energy, it is in an unstable excited state. The excess energy isreleased usually in the form of electromagnetic radiation, until the atom is again in its naturalstable state. The orbital configuration and binding energy of electrons around an atom is acharacteristic feature of the atom. Therefore, frequency spectrum of the radiation emitted from anexited atom can be used as the fingerprint of atom. Such radiation is called characteristic radiation(Fig. 2) and is the basis of spectroscopy where, elements are traced in compounds using theradiation emitted.

If the radiation emitted during de-excitation of electrons has the wavelength near visible lightthe phenomenon is called luminescence. The process of de-excitation in such atoms is usually veryfast (10–9 – 10–5 s) and is termed as fluorescence, but in some compounds emission is slow (10–5 –10s) and such slow emission is called phosphorescence. In some materials increasing temperaturefacilitates the spin conversion and emission of light is known as thermo-luminescence. Suchmaterials are used in personnel dosimetry for the occupational workers handling radioactivematerial or working in radiology.

Auger ProcessWhen an exited electron leaves an orbital, electrons from outer layer rush to occupy the vacancyand mostly the excess energy is released in the form of a single photon. However, there aresituations, when the excess energy knocks out one of the outer orbital electrons. The outcome ofthis radiation less process is the creation of an ion, and an electron known as Auger electron.Auger electron process is alternative to characteristic X-ray emission. In light elements theprobability of the phenomena is most, when a K-level vacancy is occupied by L-level electron.Usually another L-level electron is ejected. In heavy elements, the probability is more for L-leveland M-level vacancies. Auger electrons can deposit very large energy within a short range (highLET) in biological tissues. The Auger electron-emitting nuclide can covalently bind to DNA, andcause double strand breaks and cell death. Such nuclides have potential therapeutic applications innuclear medicine.


Nuclear Structure

HistoryHenri Becquerel (1896), intrigued by Roentgen’s discovery was looking for X-rays inphosphorescent Uranium salts. He accidentally discovered a new form of radiation, different fromboth phosphorescent light and X-rays. It marked the beginning of the field of nuclear physics.Marie and Pierre Curie (1898), showed that such rays were not unique to Uranium and discoveredthe new elements Polonium and Radium. They coined the term Radioactivity by which thephenomenon has been known ever since. Four years later Ernest Rutherford and Frederick Soddyfound that, substances like Uranium and Thorium transmute naturally into other elements.

Soon after it was shown that, there are three kinds of radiations emitted from radioactivematerials, which were called , and rays. A year after the discovery of the electron, -rayswere found to be electrons of very high velocity. After Bohr atomic model, it became obvious thatthe energy of – particles is too high to be of atomic origin, and that these electrons must havecome from the nucleus. Likewise -rays are much more energetic than atomic X-rays, andtherefore, must be of nuclear origin. It was eventually learned that -rays are just helium atomswithout electrons, each carrying two units of positive charges.

In 1917 Rutherford succeeded to split the nitrogen atom, and discovered the proton. He alsomade a hypothesis about the existence of a heavy neutral particle inside the atom. Nevertheless,the journey from the hypothesis to the discovery of a “missing particle” was quite long. Chadwickultimately discovered this particle as neutron in 1932. This wonderful discovery boosted researchin nuclear physics. A nucleus is made up of positively charged protons and neutral neutrons,which are collectively called nucleons. The nucleons are made up of quarks, and have a radius ofabout 0 8 fm. (10–15 m).

In every atom the number of the electrons is equal to the number of the protons, so atoms areelectrically neutral. The chemical properties of an atom are exclusively dependent on the numberof electrons. Hence, the number of protons determines, which chemical element the atom belongsto. The elements in the “Periodic table” are sorted by the number of the protons present in theiratomic nuclei. The number of neutron has nothing to do with the chemical properties. Atoms,which have similar atomic number but different neutron number (isotopes), are chemicallyidentical. Although some physical properties are different they are essentially the same element.The number of proton in an atom is called atomic number and represented by Z. The total numberof nucleons is the mass number of the nucleus (represented by A). The difference, A-Z is theneutron number, N. Nuclides with the same mass number are called isobars and nuclides with thesame neutron numbers are called isotones.

There are several notations to summarize nuclear composition of an atom. The most commonis A

Z NX , where X represents the chemical symbol of the element. Chemical symbol and atomic

number carry the same information and neutron number can be determined from difference of Aand Z. Hence, for the sake of simplicity the notation is briefed to AX, that is quite comprehensible.For example, 137Cs, where 137 is the mass number (A + Z), the symbol Cs represent 55th element(Z = 55) in periodic table. The neutron number can easily be calculated (A – Z = 82).


Table 2: Mass and charge of proton, neutron and electron

Particle Symbol Charge* Mass** Mass (kg) Energy(MeV) Relative mass

Proton p + 1 1.007276 1.6726 × 10–27 938.272 1836

Neutron n 0 1.008665 1.6749 × 10–27 939.573 1839

Electron e– – 1 0.000548 9.1093 × 10–31 0.511 1

*Unit charge = 1.6 × 10–11 coulombs**Mass expressed in Universal mass unit (mass of 1/12 of 12C atom )(Data from “Particles and nuclei 1999)

Nuclear ForcesProtons in a nucleus are fairly at close distances ( 10–15 m). This closeness results in anenormously strong repulsive force between protons. They still remain within the nucleus, due tothe existence of a very strong attractive force between nucleons, that dominates the repulsiveforce between protons and makes the atom stable. The force must be effective in very short range,and neutrons have an essential role in creating such force. Without neutrons, protons cannot stayin close distances inside the nucleus.

In 1935, Yukawa proposed that, the short-range strong force came about from the exchangeof particles that he called mesons. The strong nuclear force is one of the four fundamental forcesin nature, that is created between nucleons by the exchange of mesons. This exchange can becompared to constantly hitting a tennis ball back and forth between two people. As long as thismeson exchange is happening, the strong force holds the nucleons together. Neutrons alsoparticipate in the meson exchange, and are even a bigger source of strong force. Neutrons have nocharge so they approach other nuclei without adding extra repulsive force, and meanwhile theyincrease the average distance between protons and help to reduce the repulsion between themwithin the nucleus.

In a nucleus there is another force that is much weaker with a much shorter range called weekforce. It is thought to be responsible for beta decay and radioactivity (discussed in later chapters).Though our knowledge about an atom is quite clear, it is not so for a nucleus. Table 3 summarizesthe forces that are known as fundamental forces of nature. The electromagnetic force and theweak nuclear force can be described as two different aspects of a single electromagnetic force.

Table 3: Fundamental forces of nature

Force RelativeStrength

Comments

Strong (nuclear) 1 Attractive force between nucleons, holds nucleus together

Electromagnetic(coulomb)

10–2 Force between charged particles, holds atom together, responsible forchemical interactions

Weak 10–13 Mediates beta decay

Gravitational 10–39 Forces between objects due to their masses, not significant at atomic level


Nuclear Binding Energy and Mass DefectNuclear strong force is the resultant of phenomenon known as mass defect. Direct measurementsshow that the mass of a nucleus is always less than the sum of the individual masses of theconstituent protons and neutrons. Using the Einstein relationship, the deficient mass m is exactlyequal to the energy required to separate the nucleons or binding energy Eb of the nucleus.

Eb = m.c2 ... (8)

Where c is the speed of the light in vacuum.

The mass associated with binding energy is carried away in the form of energy, that isreleased during assembly of neutrons and protons. The nuclear mass defect, a slightly lowermass of the nucleus compared to the sum of the masses of its constituent matter, is due to thenuclear binding energy holding the nucleus together. The mass defect is the measure of thenuclear binding energy (E = mc2). The average binding energy per nucleon is a measure ofnuclear stability. The higher the average binding energy, the more stable is the nucleus.

Suggested Reading1. Physics in Nuclear Medicine, S.R. Cherry, J.A. Sorenson, M.E. Phelps, 3rd edition, Saunders,

Philadelphia, USA, 2003.2. Introductory Physics of Nuclear Medicine, R. Chandra, Lea & Febiger, Publisher, Philadelphia, USA,

1992.3. Fundamental Physics of Radiology, W.J. Meredith and J.B. Massey, John Wright & Sons Limited,

Bristol, UK, 1974.4. The Physics of Radiology by H.E. Johns & J.R. Cunningham, Charles C. Thomas Publisher,

Springfield, 1969.5. Nuclear Medicine, R. Henkin (ed.) Mosby, 1996.

basic physics and radiation · 2019-05-16 · basic physics and radiation safety in nuclear...

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