Resident Physics Lecture http://www.radiology.mcg.edu/radiologyphysics/ Christensen, Chapter 1 Radiation George David Associate Professor Department of Radiology Medical College of Georgia

Whoops, I think I just lost an electron Physics Can Be Fun Atom #1 Atom #2 Whoops, I think I just lost an electron Are you sure? Atom #1 Atom #2 Yeah, I’m positive groan George David Associate Professor Department of Radiology Medical College of Georgia

Quicky Science Review

Memorize this. That’s an order! Abbreviations Memorize this. That’s an order! 109 giga G (billion) 106 mega M (million) 103 kilo K (thousand) 10-1 deci d (tenth) 10-2 centi c (hundredth) 10-3 milli m (thousandth) 10-6 micro m (millionth) 10-9 nano n (billionth) 10-12 pico p (millionth millionth) Angstrom = A = 10-10 m

Energy Aside Kinetic Energy Potential Energy Energy of an object by virtue of its speed K.E. = (1/2) X mv2 m  mass v  velocity Potential Energy Energy of an object by virtue of its position

What’s the Smallest Thing that is Sugar? Divide, divide, divide The smallest entity that is still sugar is the sugar molecule

What’s in that Sugar Molecule? Different color balls? No! Atoms

Interesting Fact You Already Knew There are only 92 naturally occurring types of atoms HOWEVER There are zillions of different types of molecules That’s way cool.

Ever Seen This?

Composition of the Atom Protons Neutrons Electrons + -

Protons Positive charge Live in nucleus +

Neutrons No charge (free?) Live in nucleus Ever-so-slightly more mass than proton Better than oldtrons?

Electrons Negative charge Found outside nucleus Exist only in designated shell locations Weighs 1/1836th as much as proton - - +

Atomic Number Helium Also Helium # protons Defines element & its properties Color State Helium is helium because it has 2 protons # neutrons does not affect chemistry Helium Also Helium + + - + - + - -

Atomic Weight # protons + # neutrons # nucleons Specific elements often found with multiple atomic weights (isotopes) Always the same # protons Different # neutrons For a particular element, some isotopes may be stable, others unstable (radioactive) Helium Atomic Weight=4 Helium Atomic Weight=3 + + - + - + - -

Atomic Mass Unit (amu) Particle Amu Proton 1.00728 Neutron 1.00867 Nominally 1 amu = the weight of a proton or neutron Officially 1 amu = 1/12 the weight of a carbon-12 atom Atomic # = 6 Particle Amu Proton 1.00728 Neutron 1.00867 Electron .000549

Atomic Weight (# protons + # neutrons) Atomic Symbol Atomic Weight (# protons + # neutrons) He 2 4 + + - Atomic # (# protons) -

How Many Electrons? In a neutral atom (not negative or positive) # electrons = # protons + + - -

Unlike charges attract Charge Theory Unlike charges attract Like charges repel + + + -

Coulomb Forces + - k q1 q2 F = ------------ Equation r2 F = Coulomb force q’s = charges of the two objects k = constant r = distance between objects

Coulomb Equation Story k q1 q2 F = ------------ r2 Force proportional to the magnitude of the charges + + - + + + + - +

Coulomb Equation Story Force falls off with the square of distance Twice as far: one quarter the force Three times as far: one ninth the force k q1 q2 F = ------------ r2 + + - - + -

Why Doesn’t the Nucleus Fly Apart with all those + Charges? ??????????????

“c”, the speed of light, is a really big number. E = mc2 Energy & mass are equivalent. A little bit of mass is equivalent to a whole lot of energy. “c”, the speed of light, is a really big number.

What do two cars & three trains weigh? Total Mass Car weighs 2 oz. Train weights 3 oz. What do two cars & three trains weigh?

Total Mass But not in the nucleus!!! + + + + mass of the total = mass of the parts + + + + But not in the nucleus!!!

< Mass Defect mass of the total < mass of the parts + - + - < Where did the mass go?

Where did the mass go? Binding energy of the nucleus of course Mass Defect + - + - < Where did the mass go? Binding energy of the nucleus of course

And this is what we call radioactivity. Nuclear Stability How can unstable nuclei become more stable? Reduce energy Ejecting energy (photon) OR Ejecting mass And this is what we call radioactivity. Gamma Beta Alpha

Nuclear Stability Displays # protons & # neutrons for stable isotopes Stable nuclei found in nature Reference line where # protons = # neutrons

Nuclear Stability Related to neutron to proton ratio Too high or too low = unstable Decay tends to try to “center” the ratio Ratio close to 1:1 for low atomic #’s Ratio climbs with atomic # 1.6:1 for lead High atomic #’s tend to be less stable

Some Definitions Isotopes Isotones Isobars Isomers Isobergs Nuclides with same # protons Isotones Nuclides with same # neutrons Isobars Nuclides with same atomic weight Isomers Nuclides with same # protons & neutrons but different energy states Isobergs Not really

Examples ISOTOPES: I ISOTONES: Cs Xe I ISOBARS: Xe Cs I ISOMERS: Tc 125 127 131 53 ISOTONES: Cs 133 55 Xe 132 54 I 131 53 ISOBARS: Xe 131 54 Cs 55 I 53 ISOMERS: Tc 99M 99 ISOCREAM

Orbital Electrons X Electrons “-” charge very small mass compared to protons / neutrons Electrons reside only at certain energy levels or Shells Designations start at K shell K shell closest to nucleus L shell next closest Shells proceed up from K, L, M, N, etc. Except for K shell, all shells contain sub-shells L K + - + + + X - -

Electrons & Shells Atom mostly empty space If atom were a baseball stadium, nucleus would be size of baseball Nucleus contains almost all of atom’s mass Electron shells determine element’s chemical properties

Shell Capacities Shell Electron Capacity (2x2) 1 (k) 2 2 (l) 8 3 (m) 18 4 (n) 32 5 (o) 50 6 (p) 72 7 (q) 98

Binding Energy Definition Energy required to remove orbital electron from atom Ionization Negative electrons attracted to positive nucleus more binding energy for shells closer to nucleus K shell has highest binding force higher atomic # materials (higher Z) result in more binding energy more positive charge in nucleus L - K + + + + - - -

Electron Shells electrons attempt to reside in lowest available energy shell L K + + + + - - -

Electron Shells electrons attempt to reside in lowest available energy shell L K - + + + + - -

The Shell Game Electrons can move from shell to shell * Electrons can move from shell to shell to move to higher energy shell requires energy input equal to difference between the binding energy of the two shells Excitation Deposit energy here L Requires energy input! K - + + + + - -

The Shell Game Electron in higher shell & gap in lower shell = Potential Energy An atom with a gap in a lower shell is unhappy (unstable) Electrons will attempt to drop to lower shells to fill the gap K L + -

The Shell Game For atom to move to lower energy shell, atom must release energy Equal to difference between binding energy of shells Form of energy release characteristic x-rays L - K - + + + + - Energy released

Electromagnetic Radiation Transport of energy through space Properties of EM are combination of electric fields magnetic fields X-rays are one form of electromagnetic radiation No transport medium required

Electromagnetic Radiation Examples x-rays radio waves microwaves visible light radiant heat

Electromagnetic Radiation EM sometimes act like particles, sometimes like waves Particle concept explains radiation interactions with matter Wave concept explains refraction diffraction polarization

Particle concept (cont) X-rays are discrete bundles of energy quantum or photon Photon Energy proportional to frequency higher frequency => higher energy energy measured in electron volts (eV) energy gained by electron accelerated by 1 volt potential Energy = Planck’s Constant X Frequency E = hn

Velocity = Wavelength X Frequency Wave Properties of EM Wavelength distance between successive waves Frequency number of waves passing a particular point per unit time Velocity (“c”) of light / x-rays 186,000 miles/second OR 3 X 108 meters/second Wavelength & frequency inversely proportional Velocity = Wavelength X Frequency c = l X n

Wavelengths and EM Low energy High energy Highest wavelength = lowest frequency Radio Infrared Visible light Ultraviolet Soft x-rays Diagnostic x-rays Therapeutic x-rays & gammas Low energy High energy Lowest wavelength = highest frequency Velocity = Wavelength X Frequency c = l X n

Energy vs. Wavelength as Equations Energy = Planck’s Constant X Frequency E = hn but Frequency = Speed of Light / Wavelength n = c / l so E = hc / l Energy (keV) = 12.4 / Wavelength (in Angstroms) E = 12.4 / l