MEDICAL IMAGING Dr Hugh Blanton ENTC 4390 Radiation
MEDICAL IMAGING Dr. Hugh Blanton ENTC 4390
Radiation and the Atom
What is Radiation? Dr. Blanton - ENTC 4390 - RADIATION 3
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 4390 - RADIATION 4
Dr. Blanton - ENTC 4390 - RADIATION 5 Page 19
Ionizing Radiation Hits An Atom Ejected Electron Incoming Photon Dr. Blanton - ENTC 4390 - RADIATION 6
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 4390 - RADIATION 7
Alpha Particles: 2 neutrons and 2 protons: They travel short distances, have large mass Only a hazard when inhaled Dr. Blanton - ENTC 4390 - RADIATION 8
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 4390 - RADIATION 9
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 4390 - RADIATION 10
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 4390 - RADIATION 11
***Electron-Volts (e. V)*** q When talking about subatomic particles, and individual photons, energies are very small (~10 -12 or smaller). q It’s cumbersome to always deal with these powers of 10. q We introduce a new unit of energy, called the electron-volt (e. V). q An [e. V] is equivalent to the amount of energy a single electron gains when it is accelerated across a voltage of 1 [V]. q Your TV tube accelerates electrons using 20, 000 [V] = 20 [k. V]. GPE 10[J] 1 kg Electric Potential 0 [V] 1 m 0 [k. V] Dr. Blanton - ENTC 4390 - 0 [J] RADIATION -20 [k. V] 12 + - -20 [k. V]
More on [e. V] How much energy does an electron gain when it is accelerated across a voltage of 20, 000 [V] ? [V] [e. V] E = 20, 000 [e. V] is a unit of “Potential” is a unit of Energy (can be converted to [J]) How can you convert [e. V] to [J] ? Not too hard… the conversion is: Dr. Blanton - ENTC 4390 - 1 [e. V] = 1. 6 x 10 -19 [J] RADIATION 13
More on [e. V] So, let’s do an example ! Convert 20 [ke. V] to [J]. Since the “k” == kilo = 1000 = 103, 20 [ke. V] = 20, 000 [e. V] = 2 x 104 [e. V] =1 It’s a lot easier to say “ 20 [ke. V]” than 3. 2 x 10 -15 [J] ! Dr. Blanton - ENTC 4390 - RADIATION 14
Even more on [e. V] So, [e. V] 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 [e. V] = 1. 6 x 10 -19 [J] (can be used to go back & forth between these two energy units) 1 [ke. V] = 1000 [e. V] = 103 [e. V] 1 [Me. V] = 1, 000 [e. V] = 106 [e. V] 1 [Ge. V] = 1, 000, 000 [e. V] = 109 [e. V] Dr. Blanton - ENTC 4390 - RADIATION “k = kilo (103)”” “M = mega (106)” “G = giga (109)” 15
Example 1 A Cobalt-60 nucleus is unstable, and undergoes a decay where a 1173 [ke. V] photon is emitted. From what region of the electromagnetic spectrum does this come? Dr. Blanton - ENTC 4390 - RADIATION 16
The energy is 1173 [ke. V], which is 1173 [ke. V] = 1173 x 103 [e. V] = 1. 173 x 106 [e. V]. * First convert this energy to [J], E = 1. 173 x 106 [e. V] * (1. 6 x 10 -19 [J] / 1 [e. V]) = 1. 88 x 10 -13 [J] * Now, to get the wavelength, we use: E = hc/l, that is l = hc/E. So, l = 6. 63 x 10 -34[J s]*3 x 108[m/s]/1. 88 x 10 -13 [J] = 1. 1 x 10 -12 [m] * Now, convert [m] to [nm], 1. 1 x 10 -12 [m] * (109 [nm] / 1 [m]) = 1. 1 x 10 -3 [nm] It’s a GAMMA Ray Dr. Blanton - ENTC 4390 - RADIATION 17
Example 2 An electron has a mass of 9. 1 x 10 -31 [kg]. What is it’s rest mass energy in [J] and in [e. V]. E = mc 2 = 9. 1 x 10 -31*(3 x 108)2 = 8. 2 x 10 -14 [J] Now convert to [e. V] What is an electron’s rest mass? According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 m = E / c 2 = 0. 51 [Me. V/c 2] Dr. Blanton - ENTC 4390 - RADIATION 18
Example 3 A proton has a mass of 1. 67 x 10 -27 [kg]. What is it’s rest mass energy in [J] and in [e. V]. E = mc 2 = 1. 67 x 10 -27 *(3 x 108)2 = 1. 5 x 10 -10 [J] Now convert to [e. V] What is a proton’s rest mass? According to Einstein, m = E/c 2, that is: [mass] = [Energy] / c 2 m = E / c 2 = 940 [Me. V/c 2] Dr. Blanton - ENTC 4390 - RADIATION 19
Proton vs Electron Mass How much more massive is a proton than an electron ? Ratio = proton mass / electron mass = 940 (Me. V/c 2) / 0. 51 (Me. V/c 2) = 1843 times more massive You’d get exactly the same answer if you used: electron mass = 9. 1 x 10 -31 [kg] Proton mass = 1. 67 x 10 -27 [kg] Using [Me. V/c 2] as units of energy is easier… Dr. Blanton - ENTC 4390 - RADIATION 20
Neils Bohr and the Quantum Atom Circa q Pointed out serious problems with Rutherford’s atom Ø Electrons should radiate as they orbit the nucleus, and in doing so, lose energy, until they spiral into the nucleus. 1910 -1925 ØAtoms only emit quantized amounts of energy (i. e. , as observed in Hydrogen spectra) q He postulated Ø Electric force keeps electrons in orbit Ø 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 Dr. Blanton - ENTC 4390 - RADIATION 1885 -1962 21
Bohr’s Picture of the Atom Before Electrons circle the nucleus due to the Electric force n = 5 4 3 2 1 Electron in excited state (n=5) Allowed Orbits After Radiated photon 5 Electron in lowest “allowed” energy level (n=1) 4 3 2 1 Electron falls to the lowest energy level Note: There are many more energy levels beyond n=5, they are omitted for simplicity Dr. Blanton - ENTC 4390 - RADIATION 22
Atomic Radiation It is now “known” that when an electron is in an “excited state”, it spontaneously decays to a lower-energy stable state. E 5 > E 4 > E 3 > E 2 > E 1 One example could be: Energy Electron in excited state (higher PE) Energy E 5 n=5 E 4 n=4 E 3 n=3 E 2 n=2 E 1 n=1 Before Dr. Blanton - ENTC 4390 - RADIATION Electron in lowest state (lower PE) After 23
The difference in energy, DE, is given by: DE = E 5 – E 1 = hn = Ephoton h = Planck’s constant = 6. 6 x 10 -34 [J s] n = frequency of light [hz] The energy of the light is DIRECTLY PROPORTIONAL to the frequency, n. Recall that the frequency, n, is related to the wavelength by: c = nl (n = c / l) So, higher frequency higher energy lower wavelength This is why UV radiation browns your skin but visible light does not ! Dr. Blanton - ENTC 4390 - RADIATION 24
Hydrogen atom energy “levels” Quantum physics provides the tools to compute the values of E 1, E 2, E 3, etc…The results are: En = -13. 6 / n 2 5 3 1 4 Energy Level Energy En (e. V) 2 1 -13. 6 2 -3. 4 3 -1. 51 4 -0. 85 5 -0. 54 These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE Dr. Blanton - ENTC 4390 - RADIATION 25
Hydrogen atom energy “levels” So, the difference in energy between the 3 rd and 1 st quantum state is: Ediff = E 3 – E 1 = -1. 51 – (-13. 6) = 12. 09 (e. V) When this 3 1 atomic transition occurs, this energy is released in the form of electromagnetic energy. Dr. Blanton - ENTC 4390 - RADIATION 26
Example 4 In the preceding example, what is the frequency, wavelength of the emitted photon, and in what part of the EM spectrum is it in? E = 12. 1 [e. V]. First convert this to [J]. Since E = hn n = E/h, so: n = E/h = 1. 94 x 10 -18 [J] / 6. 6 x 10 -34 [J s] = 2. 9 x 1015 [1/s] = 2. 9 x 1015 [hz] Dr. Blanton - ENTC 4390 - RADIATION 27
Example 4 l = c/n = (3 x 108 [m/s]) / (2. 9 x 1015 [1/s]) = 1. 02 x 10 -7 [m] = 102 [nm] This corresponds to low energy X-rays ! Dr. Blanton - ENTC 4390 - RADIATION 28
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