MEDICAL IMAGING
Dr. Hugh Blanton
ENTC 4390
Radiation and the Atom
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What is Radiation?
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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
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Ionizing Radiation Hits An Atom
Incoming
Photon
EjectedElectro
n
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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.
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Alpha Particles: 2 neutrons and 2 protons:
They travel short distances, have large massOnly a hazard when inhaled
Alpha Particles
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Beta ParticlesBeta Particles: Electrons or positrons having small mass and variable energy. Electrons form when a neutron transforms into a proton and an electron:
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Gamma RaysGamma 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.
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X-RaysX-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
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***Electron-Volts (eV)*** When talking about subatomic particles, and individual photons,energies are very small (~10-12 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 gainswhen 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 kgGPE
1 m0 [V]
-20 [kV]
+
-
ElectricPotential
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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] = 1.6x10-19 [J]
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More on [eV]So, let’s do an example ! Convert 20 [keV] to [J]. Since the “k” == kilo = 1000 = 103, 20 [keV] = 20,000 [eV] = 2x104 [eV]
It’s a lot easier to say “20 [keV]” than 3.2x10-15 [J] !
-194 151.6x10 [J]2x10 [eV] 3.2 10 [J]
1 [eV]x
=1
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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] = 1.6x10-19 [J] (can be used to go back & forth between these two energy units)
1 [keV] = 1000 [eV] = 103 [eV] “k = kilo (103)””
1 [MeV] = 1,000,000 [eV] = 106 [eV] “M = mega (106)”
1 [GeV] = 1,000,000,000 [eV] = 109 [eV] “G = giga (109)”
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Example 1A 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?
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The energy is 1173 [keV], which is 1173 [keV] = 1173x103 [eV] = 1.173x106
[eV].
* First convert this energy to [J],
E = 1.173x106 [eV] * (1.6x10-19 [J] / 1 [eV]) = 1.88x10-13 [J]
* Now, to get the wavelength, we use: E = hc/, that is = hc/E.
So, = 6.63x10-34[J s]*3x108[m/s]/1.88x10-13 [J] = 1.1 x 10-12 [m]
* Now, convert [m] to [nm], 1.1 x 10-12 [m] * (109 [nm] / 1 [m]) = 1.1x10-3 [nm]
It’s a GAMMA Ray
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Example 2An electron has a mass of 9.1x10-31 [kg].
E = mc2 = 9.1x10-31*(3x108)2 = 8.2x10-14 [J] Now convert to [eV]
-14 5
-19
1 [eV]8.2x10 [J] 5.1x10 [eV]=0.51 [MeV]1.6x10 [J]
What is an electron’s rest mass?
m = E / c2 = 0.51 [MeV/c2]
According to Einstein, m = E/c2, that is:[mass] = [Energy] / c2
What is it’s rest mass energy in [J] and in [eV].
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Example 3A proton has a mass of 1.67x10-27 [kg].
E = mc2 = 1.67x10-27 *(3x108)2 = 1.5x10-10 [J] Now convert to [eV]
-10 8
-19
1 [eV]1.5x10 [J] 9.4x10 [eV]=940 [MeV]1.6x10 [J]
What is a proton’s rest mass?
m = E / c2 = 940 [MeV/c2]
According to Einstein, m = E/c2, that is:[mass] = [Energy] / c2
What is it’s rest mass energy in [J] and in [eV].
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Proton vs Electron MassHow much more massive is a proton than an electron ?
Ratio = proton mass / electron mass
= 940 (MeV/c2) / 0.51 (MeV/c2) = 1843 times more massive
You’d get exactly the same answer if you used:
electron mass = 9.1x10-31 [kg]
Proton mass = 1.67x10-27 [kg]
Using [MeV/c2] as units of energy is easier…
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Neils Bohr and the Quantum Atom
1885-1962
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 froman outer orbit to an inner orbit and the energydifference is given off as a radiation.
Awarded the Nobel Prize in 1922
Circa 1910-1925
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Electrons circle the nucleus due to the Electric force
Bohr’s Picture of the Atom
Allowed Orbits
12
34
5n =
Electronin lowest“allowed”
energy level(n=1)
Electronin excited
state(n=5)
Before
12
34
5
Electron falls to the lowest
energy level
AfterRadiatedphoton
Note: There are many more energy levels beyond n=5, they are omitted for simplicity
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Atomic RadiationIt is now “known” that when an electron is in an “excited state”,it spontaneously decays to a lower-energy stable state.
Beforen = 1
n = 2
n = 3
n = 4
n = 5
Energy Electronin excited
state(higher
PE)
E5
E4
E2
E3
E1
E5 > E4 > E3 > E2 > E1
Aftern = 1
n = 2
n = 3
n = 4
n = 5
Energy Electronin lowest
state(lower PE)
E5
E4
E2
E3
E1
One example could be:
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The difference in energy, E, is given by:
E = E5 – E1 = hphoton
h = Planck’s constant = 6.6x10-34 [J s] = frequency of light [hz]
The energy of the light is DIRECTLY PROPORTIONAL to the frequency, .
Recall that the frequency, , is related tothe wavelength by:
c = c
So, higher frequency higher energy lower wavelength
This is why UV radiation browns your skinbut visible light does not !
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Hydrogen atom energy “levels”Quantum physics provides the tools to compute the values ofE1, E2, E3, etc…The results are:
En = -13.6 / n2
Energy Level Energy En (eV)
1 -13.62 -3.43 -1.514 -0.855 -0.54
These results DO DEPEND ON THE TYPE OF ATOM OR MOLECULE
12
34
5
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Hydrogen atom energy “levels”
So, the difference in energy between the 3rd and 1st quantum state is:
Ediff = E3 – E1 = -1.51 – (-13.6) = 12.09 (eV)
When this 3 1 atomic transition occurs, this energy is released in the form of electromagnetic energy.
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Example 4
E = 12.1 [eV]. First convert this to [J].
-19181.6x10 [J]12.1 [eV] 1.94 10 [J]
1 [eV]x
Since E = h = E/h, so:
= E/h = 1.94x10-18 [J] / 6.6x10-34 [J s] = 2.9x1015 [1/s] = 2.9x1015 [hz]
In the preceding example, what is the frequency, wavelength of theemitted photon, and in what part of the EM spectrum is it in?
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Example 4
= c/= (3x108 [m/s]) / (2.9x1015 [1/s]) = 1.02x10-7 [m] = 102 [nm]
This corresponds to low energy X-rays !
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