Radiation physicsLecture 1

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Radiation physicsLecture 1

Bikramjit Chakrabarti, MD, DNB

• Structure of atoms• Production of X-rays

• Nuclear transformations

ENGLAND: Rutherford

DENMARK:Niels Bohr

FRANCE: Curie

GERMANY:Einstein

ITALY:Fermi

GERMANY:Planck

A brief history of discovery of atomic structure

• Discovery of cathode ray, X-ray• Discovery of radioactive elements – natural

and artificial,• Discovery of nucleus, atomic and fundamental

particles.

John Dalton (1803)1. All elements are composed of atoms, which are indivisible and indestructible particles.2. All atoms of the same element are exactly alike; in particular, they all have the same mass.3. All atoms of different elements are different; in particular, they have different masses.4. Compounds are formed by the joining of atoms of two or more elements. In any compound atoms combined only in small whole-number ratios, such as 1:1, 1:2, 2:1, 2:3, to form compounds.

Cathode Ray - Johann Hittorf & Eugen Goldstein (1869)

Cathode ray causing fluorescence on glass wall. Shadow of fan is deviated when magnetic field is applied.

Cathode ray

•Traveled in a straight line•Their path could be "bent" by the influence of magnetic or electrical fields•A metal plate in the path of the "cathode rays" acquired a negative charge•Produce fluorescence

Wilhelm Roentgen (1895)

New type of ray that1.Could pass unimpeded through

many objects2.Were unaffected by magnetic or

electric fields3.Produced an image on

photographic plates (i.e. they interacted with silver emulsions like visible light)

4.Produced fluorescence5.Ionized a gas

X ray production

Vacuum glass tube

Cathode made of tungsten filament

High voltage (10V, 6A) for TI E

Thick copper

rod

High Z,High melting

point

Cu: absorbs stray electrons,W: absorbs stray XR

Coolidge tube

• Focal spot: Line focus (a sinѲ)• Heel effect• Circuitry: step-up transformer

and rheostat• Tube voltage measured by

sphere gap method.• Efficiency= OE/IE,• Output = exposure = ionization

produced, depends on voltage.

• The probability of bremsstrahlung emission is proportional to the value of Z2

• Fluorescent yield: Probability to produce characteristic X-rays.

• Typical anode currents, depending on the examination mode, are <10 mA in fluoroscopy and 100 mA to >1000 mA in single exposures.

• The typical range of tube voltages is 40–150 kV for general diagnostic radiology and 25–40 kV in mammography.

Properties of X-ray producedHeterogeneous: The energy of the Bremsstrahlung photon depends on • the attractive Coulomb forces and hence on the distance of the electron

from the nucleus.• Energy of incident electrons Self-filtration: X rays are not generated at the surface but within the

target, resulting in an attenuation of the X ray beam. This self-filtration appears most prominent at the low energy end of the spectrum. Additionally, characteristic radiation shows up if the kinetic electron energy exceeds the binding energies. L radiation is totally absorbed by a typical filtration of 2.5 mm Al. For tungsten targets, the fraction of K radiation contributing to the total energy fluence is less than 10% for a 150 kV tube voltage.

Contd..• For mammography, other anode materials such as molybdenum (Z =

42) and rhodium (Z = 45) are frequently used. For such anodes, X ray spectra show less contribution by bremsstrahlung but rather dominant characteristic X rays of the anode materials. This allows a more satisfactory optimization of image quality and patient dose. In digital mammography, these advantages are less significant and some manufacturers prefer tungsten anodes.

• Off focus radiation: Extrafocal radiation can contribute up to ~10% of the primary X ray intensity. Sometimes, parts of the body are imaged outside the collimated beam by off focus radiation. Off focus radiation also increases patient dose. The best position for a diaphragm to reduce off focus radiation is close to the focus.

Antonio Henri Becquerel (1896)Radioactivity – radiation from nucleus

Photographic plate with potassium uranyl sulfate crystals showed a dark spot even when stored in dark.

JJ THOMSON (1897) – CRT experiment: Discovery of electron

• Electron was discovered by J. J. Thomson in 1897 when he was studying the properties of cathode ray.• J. J. Thomson measured the charge-by-mass-ratio (e/m) of cathode ray particle using deflection in both electric and magnetic field.• em=−1.76×108em=−1.76×108 coulomb per gram• Thompson determined the charge to

mass ratio for the electron, but was not able to determine the mass of the electron.

Marie Sklodowska Curie & Pierre Curie(1898) discovered radium

In 1899, Rutherford had discovered alpha and

beta "rays" from uranium.

Now, today we know they are not rays, they are particles; alpha is a nucleus

of helium and beta is an electron.

Ernest Rutherford (1899)

Albert Einstein (1905)Nobel prize for work on photo-electric effect !!

• The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),

• The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

• E= mc2. The faster an object moves, the more massive it becomes. That means that, in theory, no object can ever reach 100 percent of the speed of light because its mass would become infinite.

• The general theory of relativity (1916): acceleration distorts the shape of time and space.

Ernest Rutherford (1908)

But why electrons do not radiate energy to spiral into the nucleus?

Line spectra not explained

Ernest Rutherford (1908)

1. Almost all the incident alpha particles go straight and are scarcely scattered.2. Only occasionally such a large-angle scattering through an angle greater than 90 degrees or near 180 degrees occurs.3. The scattering rate depends on the atomic weight of the target; the more the atomic weight, the larger the probability.

Concept of proton (in anode or canal rays) – Goldstein (1908)

• The lightest ones, formed when there was some hydrogen gas in the tube, were calculated to be about 1840 times as massive as an electron.Cathode: Perforated,

Potential difference: several thousands.

Niels Bohr (1913) - postulates• Electrons can exist only in orbits

where angular momentum = multiple of Planck constant/2π

• No energy is gained or lost when in this permissible orbits.

• Radiation is absorbed or emitted when an electron moves from one orbit to another. And the energy change E = E2 – E1

Niels Bohr (1913) – failed to explain• Incorrect value for the ground state orbital

angular momentum.• Dual nature of electron and the Heisenberg

Uncertainty Principle because it considers electrons to have both a known radius and orbit.

• No explanation of fine structure of spectra -Existence of additional quantum numbers.

• Poor predictions regarding the spectra of larger atoms.

• Does not explain fine structure and hyperfine structure in spectral lines.

• No explanation for Zeeman Effect and Stark Effect.

Arnold Somerfield• He introduced the 2nd quantum

number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory.

• Elliptical orbit• Sub-shell s,p,d,f• Modification of angular

momentum as given by Bohr.

Max Karl Ernst Ludwig Plank (1918)

• Worked on thermodynamics.• Energy did not flow in a

steady continuum, but was delivered in discrete packets Planck later called quanta.

• Planck's constant (the proportion of light's energy to its wave frequency, or approximately

h = 6.626 x 10-34 J-sec).

সত্যে��ন্দ্রনাথ বসু(1924)

KOLKATA:Satyendra Nath

Bose

PHOTONS ARE BOSONS

‘GOD PARTICLES’ ARE BOSONS

The “God particle” nickname actually arose when the book The God Particle: If the Universe Is the Answer, What Is the Question? by Leon Lederman was published.

• In 1924, Satyendra Nath Bose published an article titled Max Planck's Law and Light Quantum Hypothesis. This article was sent to Albert Einstein. Einstein appreciated it so much that he himself translated it into German and sent it for publication to a famous periodical in Germany - 'Zeitschrift fur Physik'. The hypothesis received a great attention and was highly appreciated by the scientists. It became famous to the scientists as 'Bose-Einstein Theory‘.

• A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 0 K or −273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent.

89 years later....• The Nobel Prize in Physics 2013 was awarded jointly to

François Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider.

And now boson became ‘Higgs Boson’ !!!!!

Louis de Broglie (1925) – Wave-particle duality

• Wave like properties: eg refraction,• Particle like properties: eg momentum• Uncertainty about position and momentum of

wave.• E= hv = hc/λ

Erwin Schrödinger (1926) -quantum mechanical model of the atom.

• By solving the Schrödinger equation (H = E ), we obtain a set of mathematical equations, called wave functions (), which describe the probability of finding electrons at certain energy levels within an atom..

Quantum number of electrons

QUANTUM NUMBERS OF ELECTRON VALUE SPECIFIES

Principal Quantum Number (n) n = 1, 2, 3, …, ∞ Energy of an electron and the size of the orbital

Angular Momentum (Secondary, Azimunthal) Quantum Number (l)

l = 0, ..., n-1. Divides the shells into subshells (s,p,d,f)

Magnetic Quantum Number (ml) ml = -l, ..., 0, ..., +l. divides the subshell into individual orbitals

Spin Quantum Number (ms) ms = +½ or -½. Specifies the orientation of the spin axis of an electron.

• Atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light).

• Each electron in an atom is described by four different quantum numbers. The first three (n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital.

James Chadwick (1935)Discovery of neutron

Schematic diagram for the experiment that led to the discovery of neutrons by Chadwick. 4Be9+2α4 [⟶ 6C13] [⟶ 6C12]+0n1

Wolfgang Pauli (1945) Pauli exclusion principle, a quantum mechanical principle

No two electrons in the same atom can have identical values for all four of their quantum numbers.

Two electrons in the same orbital must have opposite spins.

Enrico fermi• Built first nuclear reactor• Postulated and named

neutrino,• Described weak nuclear force,• He was present at the Trinity

test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield.

• Fermions are named after him.

Commonly used -emittersISOTOPE SOURCE HALF LIFE PRODUCT ENERGY HVL Pb

88Ra226 NATURAL 1622 yrs 82Pb206 0.83 MeV 16-20 mm

27Co6027Co59 5.26 yrs 28Ni60 1.25 MeV 11 mm

55Cs13792U235 30 yrs 56Ba137 0.66 MeV 6.5 mm

77Ir19277Ir191 74 days 78Pt192 0.38 MeV 6 mm

46Pd10346Pd102 17 days 45Rh103 0.021 MeV

53I12554Xe124 60 days 52Te125 0.026 MeV 0.025 mm

53I13152Te130 8 days 54Xe131 0.364 MeV

43Tc99m42Mo98 6 hrs Tc99 0.14 MeV

PURE BETA EMITTERS

ALPHA EMITTERS NEUTRON EMITTER POSITRON EMITTER

Y90, Sr90, P32, Tl204, C14, tritium (H3)

Bi212, Pb212, Ac225, Po210, U238

Cf252 F18, C11, O15, N13

• Difference between molecule, atom, radical, ion• Size of atom: 10-10 m, nucleus: 10-15 m.• Nucleus• Atomic mass: Amu = 1/12 of C12 = 1.66 X 10-27 kg = 931.5 MeV (1 eV = 1.602 X

10-19 J)• No of atoms per gram = NA/AW

• No of electrons per gram = NA*Z/AW • Energy levels of

– Atoms– Nucleus: Mass defect = binding energy of nucleusAlpha particle requires nearly 30 Mev to cross potential barrier of nucleus.– Electron: Potential energy = negative of binding energy.

Electron• Unit negative charge:

1.602X 10-19 C• Mass: 5.48 X 10-4 amu• K,L,M shells: 2n2

• Proton:• Mass: 1.00727 amu

Identify…

• Atomic number• Mass number

• Isobar• Isotope • Isotone• Isomer• Radio-isotope vs

radio-nuclide

Fundamental particles

FERMION BOSONMatter particles12 in numberTypes: 6 quarks + 6 leptons

Odd half-integer spin of quantum units of ang mom.

Messenger particles13 in numberTypes: Photon, gluon, Weak force, gluon, gravitron etc.Integer spin (0,1,2)

Nuclear stabilityBecomes stable by nuclear conversion

• n/p ratio (N:Z ratio):1• Even-even nuclei (n,p

mutually paired)• The magic numbers are:

– proton: 2, 8, 20, 28, 50, 82, 114

– neutron: 2, 8, 20, 28, 50, 82, 126, 184

Alpha decay 2 neutrons + 2 protons ejected as helium nucleus

• Most common type of decay,• Seen in Z > 82• Alpha particles are helium nuclei,• Alpha particles have a typical kinetic energy of 5 MeV.

High n/p ratio - β- decayNeutron converts into proton along with beta ray emission

•Beta particles are emitted with a spectra of energy, from zero to a maximum value.•Average energy is 1/3 of maximum energy.

Low n/p ratioProton converts into neutron

Orbital electron capture (K capture)With characteristic X-ray emission (internal PE effect) β+ decay

With positron emission

Other processes• Internal conversion:

– Excess energy liberated as ejects orbital electron ‘hole’ characteristic x-ray produced.

• Isomeric transition– 99mTc 99Tc

Transient eq = TcSecular eq = Ra

Radio-active seriesUranium series: U238 Pb206

Actinium series: U235 Pb207

Thorium series: Th232 Pb208

Nuclear reactions• α-p reaction • α-n reaction • Proton (p,; p,n; p,d; p, reactions): • Neutron bombardment (fast neutrons required if mass difference is high):

– n- reaction (common)– n- reaction– n-p reaction

• Deuteron (fast neutron stripped):• Photo-disintegration• Fission: High Z low Z• Fusion: Low Z high Z

Remember..

• Activity = number of disintegrations per second.

• Decay constant• Half life• Mean or average life = avg time before a

particle decays.

• 1 Ci = rate of decay of 1 gram radium = 3.7 X 1010 Bq• 1 Bq = 1 dps

Activating nuclide in nuclear reactor

• Chain reaction of fission -> Neutrons generated -> bombarded to produce radio-nuclide from non-radioactive nuclide.

Lecture 2Next day

• Types of radiation.• Interaction of radiation with matter.