MEDICAL IMAGING Dr. Hugh Blanton ENTC 4390

Radiation and the Atom

Dr. Blanton - ENTC RADIATION 3 What is Radiation?

Dr. Blanton - ENTC RADIATION 4 Ionizing & Non-Ionizing Radiation Ionizing Radiation: Radiation is energy transmitted as particles or waves. Ionizing radiation has sufficient energy to dislodge orbital electrons, thereby producing ions.  Examples: alpha, beta, gamma, neutron, and x-rays  Non-Ionizing Radiation: Radiation that does not have sufficient energy to dislodge orbital electrons.  Examples: visible light, infra-red, micro-waves, radio-waves, and radar

Dr. Blanton - ENTC RADIATION 5 Page 19

Dr. Blanton - ENTC RADIATION 6 Ionizing Radiation Hits An Atom Incoming Photon Ejected Electron

Dr. Blanton - ENTC RADIATION 7 Particles and Photons Radiation can be in the form of particles or waves (photons). The most common types of ionizing radiation are alpha, beta, gamma, neutron, and x-rays. Gamma and x-ray radiation are photons. They are part of the electromagnetic spectrum and considered packets of pure energy. Alpha, beta, and neutron radiation are particles having mass. Betas are electrons and alphas are helium nuclei.

Dr. Blanton - ENTC RADIATION 8 Alpha Particles: 2 neutrons and 2 protons: They travel short distances, have large mass Only a hazard when inhaled Alpha Particles

Dr. Blanton - ENTC RADIATION 9 Beta Particles Beta Particles: Electrons or positrons having small mass and variable energy. Electrons form when a neutron transforms into a proton and an electron:

Dr. Blanton - ENTC RADIATION 10 Gamma Rays Gamma Rays (or photons): Result when the nucleus releases Energy, usually after an alpha, beta or positron transition A gamma particle is a photon. It is produced as a step in a radioactive decay chain when a massive nucleus produced by fission relaxes from the excited state in which it first formed towards its lowest energy or ground-state configuration.

Dr. Blanton - ENTC RADIATION 11 X-Rays X-Rays: Occur whenever an inner shell orbital electron is removed and rearrangement of the atomic electrons results with the release of the elements characteristic X-Ray energy

Dr. Blanton - ENTC RADIATION 12 ***Electron-Volts (eV)***  When talking about subatomic particles, and individual photons, energies are very small (~ or smaller).  It’s cumbersome to always deal with these powers of 10.  We introduce a new unit of energy, called the electron-volt (eV).  An [eV] is equivalent to the amount of energy a single electron gains when it is accelerated across a voltage of 1 [V].  Your TV tube accelerates electrons using 20,000 [V] = 20 [kV]. 0 [kV] -20 [kV] 10[J] 0 [J] 1 kg GPE 1 m 0 [V] -20 [kV] + - Electric Potential

Dr. Blanton - ENTC RADIATION 13 More on [eV] How much energy does an electron gain when it is accelerated across a voltage of 20,000 [V] ? E = 20,000 [eV] [V] is a unit of “Potential” [eV] is a unit of Energy (can be converted to [J]) How can you convert [eV] to [J] ? Not too hard… the conversion is: 1 [eV] = 1.6x [J]

Dr. Blanton - ENTC RADIATION 14 More on [eV] So, let’s do an example ! Convert 20 [keV] to [J]. Since the “k” == kilo = 1000 = 10 3, 20 [keV] = 20,000 [eV] = 2x10 4 [eV] It’s a lot easier to say “20 [keV]” than 3.2x [J] ! =1

Dr. Blanton - ENTC RADIATION 15 Even more on [eV] So, [eV] IS A UNIT OF ENERGY; It’s not a “type” of energy (such as light, mass, heat, etc). When talking about energies of single photons, or of subatomic particles, we often use this unit of energy, or some variant of it. So, 1 [eV] = 1.6x [J] (can be used to go back & forth between these two energy units) 1 [keV] = 1000 [eV] = 10 3 [eV] “k = kilo (10 3 )”” 1 [MeV] = 1,000,000 [eV] = 10 6 [eV] “M = mega (10 6 )” 1 [GeV] = 1,000,000,000 [eV] = 10 9 [eV] “G = giga (10 9 )”

Dr. Blanton - ENTC RADIATION 16 Example 1 A Cobalt-60 nucleus is unstable, and undergoes a decay where a 1173 [keV] photon is emitted. From what region of the electromagnetic spectrum does this come?

Dr. Blanton - ENTC RADIATION 17 The energy is 1173 [keV], which is 1173 [keV] = 1173x10 3 [eV] = 1.173x10 6 [eV]. * First convert this energy to [J], E = 1.173x10 6 [eV] * (1.6x [J] / 1 [eV]) = 1.88x [J] * Now, to get the wavelength, we use: E = hc/, that is = hc/E. So, = 6.63x [J s]*3x10 8 [m/s]/1.88x [J] = 1.1 x [m] * Now, convert [m] to [nm], 1.1 x [m] * (10 9 [nm] / 1 [m]) = 1.1x10 -3 [nm]  It’s a GAMMA Ray

Dr. Blanton - ENTC RADIATION 18 Example 2 An electron has a mass of 9.1x [kg]. E = mc 2 = 9.1x *(3x10 8 ) 2 = 8.2x [J] Now convert to [eV] What is an electron’s rest mass? m = E / c 2 = 0.51 [MeV/c 2 ] According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 What is it’s rest mass energy in [J] and in [eV].

Dr. Blanton - ENTC RADIATION 19 Example 3 A proton has a mass of 1.67x [kg]. E = mc 2 = 1.67x *(3x10 8 ) 2 = 1.5x [J] Now convert to [eV] What is a proton’s rest mass? m = E / c 2 = 940 [MeV/c 2 ] According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 What is it’s rest mass energy in [J] and in [eV].

Dr. Blanton - ENTC RADIATION 20 Proton vs Electron Mass How much more massive is a proton than an electron ? Ratio = proton mass / electron mass = 940 (MeV/c 2 ) / 0.51 (MeV/c 2 ) = 1843 times more massive You’d get exactly the same answer if you used: electron mass = 9.1x [kg] Proton mass = 1.67x [kg] Using [MeV/c 2 ] as units of energy is easier…

Dr. Blanton - ENTC RADIATION 21 Neils Bohr and the Quantum Atom  Pointed out serious problems with Rutherford’s atom  Electrons should radiate as they orbit the nucleus, and in doing so, lose energy, until they spiral into the nucleus.  Atoms only emit quantized amounts of energy (i.e., as observed in Hydrogen spectra)  He postulated  Electric force keeps electrons in orbit  Only certain orbits are stable, and they do not radiate energy Radiation is emitted when an e - jumps from an outer orbit to an inner orbit and the energy difference is given off as a radiation. Awarded the Nobel Prize in 1922 Circa

Dr. Blanton - ENTC RADIATION 22 Electrons circle the nucleus due to the Electric force Bohr’s Picture of the Atom Allowed Orbits n = Electron in lowest “allowed” energy level (n=1) Electron in excited state (n=5) Before Electron falls to the lowest energy level After Radiated photon Note: There are many more energy levels beyond n=5, they are omitted for simplicity

Dr. Blanton - ENTC RADIATION 23 Atomic Radiation It is now “known” that when an electron is in an “excited state”, it spontaneously decays to a lower-energy stable state. Before n = 1 n = 2 n = 3 n = 4 n = 5 Energy Electron in excited state (higher PE) E5E5 E4E4 E2E2 E3E3 E1E1 E 5 > E 4 > E 3 > E 2 > E 1 After n = 1 n = 2 n = 3 n = 4 n = 5 Energy Electron in lowest state (lower PE) E5E5 E4E4 E2E2 E3E3 E1E1 One example could be:

Dr. Blanton - ENTC RADIATION 24 The difference in energy,  E, is given by:  E = E 5 – E 1 = h  photon h = Planck’s constant = 6.6x [J s] = frequency of light [hz] The energy of the light is DIRECTLY PROPORTIONAL to the frequency,. Recall that the frequency,, is related to the wavelength by: c =  c  So, higher frequency  higher energy  lower wavelength This is why UV radiation browns your skin but visible light does not !

Dr. Blanton - ENTC RADIATION 25 Hydrogen atom energy “levels” Quantum physics provides the tools to compute the values of E 1, E 2, E 3, etc…The results are: E n = / n 2 Energy LevelEnergy E n (eV) These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE

Dr. Blanton - ENTC RADIATION 26 Hydrogen atom energy “levels” So, the difference in energy between the 3 rd and 1 st quantum state is: E diff = E 3 – E 1 = – (-13.6) = (eV) When this 3  1 atomic transition occurs, this energy is released in the form of electromagnetic energy.

Dr. Blanton - ENTC RADIATION 27 Example 4 E = 12.1 [eV]. First convert this to [J]. Since E = h  = E/h, so: = E/h = 1.94x [J] / 6.6x [J s] = 2.9x10 15 [1/s] = 2.9x10 15 [hz] In the preceding example, what is the frequency, wavelength of the emitted photon, and in what part of the EM spectrum is it in?

Dr. Blanton - ENTC RADIATION 28 Example 4  = c/  = (3x10 8 [m/s]) / (2.9x10 15 [1/s]) = 1.02x10 -7 [m] = 102 [nm] This corresponds to low energy X-rays !