07 Lesson Radioactivity 01 MP200 Radiation Physics - 2010 Duke Medical Physics Graduate Program
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Introduction
In this lesson, we will study, the processes and kinematics of, , and decays, Electron Capture, Internal Conversion and, Auger Electron
Radioactivity
The spontaneous disintegration or rearrangement of the internal structure of an unstable nucleus by emitting particles or radiation is called Radioactivity. Emitted particles and radiation from radioactivity are collectively called rays. There are three kind of rays in natural occurring radioactivity. rays, rays (electrons and positrons), rays rays are helium nucleus and can be blocked by a 0.01 mm of lead. rays are electrons or positrons and can be blocked by a 0.1 mm of lead. rays are the most penetrating and can pass through a 100 mm thick lead. In radioactive decay, Mass, energy, electric charge, linear momentum angular momentum, and nucleon numbers should be conserved. Example: Initial amount of charge = nal amount of charge after decay. Initial nucleus called parent emits a particle and produces another particle called the daughter. Daughter may be the same nucleus, in lower energy state or an entirely new nucleus.
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decay
The process of ejecting an alpha particle from a nucleus is called decay. The atomic number of the parent P decreases by 2, and the mass number decreases by 4, when the daughter D is produced.
A ZP 4 A2 D +4 He Z 2
Example:
226 88 Ra
222 Rn +4 He 86 2
Kinematics of decay Let us assume, the decay occurs in a system where the parent is at rest. P D + From the conservation of energy, M p c 2 = M D c 2 + M c 2 + KD + K KD , K = Kinetic energies, and MP , MD , M = Masses of particles Since, KD + K 0, Mp MD + M
Q - value The energy released is the disintegration energy, and it is called the Q - value. This value is equal to the dierence between the nal and the initial kinetic energies of the system.
Q = KD + K Q = (Mp MD M ) c2
From conservation of linear momentum and the Q value,
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Figure 1: decay M v = MD V 1 1 Q= M v 2 + MD V 2 2 2 Removing V from (1) and (2), 1 MD + M Q = M v 2 2 MD Since, 1 K = M v 2 2 K = and, KD = Since, MD + M A K = A4 Q A M Q MD + M MD Q MD + M (1) (2)
Decay Scheme
The nuclear transformation from parent to daughter can easily be described by a decay-scheme diagram. This diagram includes the decay mode, branching ratio, and the energy transitions.
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Conventions:
1. Arrows slanting to the left side indicate decrease in Z. 2. Arrows slanting to the right side indicate the increase in Z. 3. Wavy lines going straight down indicate the gamma emission from the nucleus. Example: The following gure shows the decay of 226 Ra. 94.4% of it decays directly to ground state emitting particles, and 5.5% of it decays to anothor lower energy state, and later to ground state by emitting gammas.
Figure 2: Decay of Spectra of -particles: discrete/mono-energetic.
226 88 Ra
decay
The process in which, the charge of the nucleus changes without any change in the number of nucleons is called -decay. There are three types of decays. 1. decay - emission of an electron. 2. + decay - emission of a positron. 3. Electron capture. In each of these decays, an additional particle called a neutrino appears as one of the decay products.
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Neutrino ( ) Neutrino was rst postulated by Pauli (1930) in order to preserve the conservation of energy and momentum of the neutron decay. n p + e + e Properties of neutrino are : 1. Rest mass 0 2. Electric charge = 0 3. Spin =
1 2
Neutrino is represented by and its anti particle by . There are three types of neutrinos and their anti particles. (e , , ) and (e , , ).
decay
In decay, a nuclide with excess neutrons, converts a neutron to a proton to gain stability. n p + e + An electron and a antineutrino are ejected.
A ZP
A+1 D +0 1 e +0 e Z 0
In this process, Conservation laws (charge, lepton number and nucleon number ) should be observed. As a result, the atomic number Z of daughter is increased by 1. Example:
12 5B 12 5B
12 C + e + e 6
has 7 neutrons and they are too many to be stable.One neutron is converted to a proton and created 12 C with 6 neutrons. 6 An electron and a antineutrino are ejected from the nucleus.
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Figure 3: decay.
Kinematics of Decay
A ZP
A+1 D +0 1 e +0 e Z 0
From conservation of energy, M p c 2 = M D c 2 + m e c 2 + Ke + K K = Kinetic energy, The Q-Value, Q = Ke + K Q = (M p M D m e ) c 2 Note: If masses Mp , MD and me are given in atomic masses. Q = [(Mp Zme ) (MD (Z + 1)me ) me ] c2 Q = [Mp MD ] c 2 Example: Consider decay,
32 15 P
32 S +0 1 e +0 e + Q 16 0 7
Using the atomic mass dierences of,
32 15 P
32 S = 1.71 M eV 16 Q = 1.71 M eV
Example: Find the maximum energy of the electron in the decay of,
3 1H
3 He + e + e 2
Solution: M3 H c 2 = M3 H c 2 + Q 2 But, Q = Ke + K Q = M3 H c 2 M3 H c 2 2 Q = (3.016050 3.016030) 931.5 M eV Q = 0.019 M eV Assume the energy of the neutrino is zero. Then, the maximum energy of the electron is 0.019 M eV . When (Mp MD ) me decay occurs.
Since, Q = MP MD , the excess energy is shared by three decay particles. The nucleus is massive and, it receives a negligible energy. The energy is shared between electron and antineutrino. Depending of the orientation of the particles, the energy of the electron in a decay can have an energy between 0 and Q. The energy spectrum of the electron in a decay is continuous. The average electron energy is about
Q . 3
Example: The gure shows the electron spectrum from decay of 32 P . The max15 imum electron energy is 1.71 M eV and the average energy is 0.698 M eV .
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Figure 4: spectrum The decay scheme for 32 P is shown in the gure. Note : Since Z is increasing, the 15 arrow is slanting to the right.
Figure 5: Decay scheme of
32 15 P
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+ Decay
The decay of a nuclide with excessive protons by emitting a positron is called a + decay. The nuclide attempts to gain stability, the by converting a proton to a neutron, and increasing the number of neutrons. p n + e+ + e As a result, the atomic number of the daughter is 1 less than that of the parent.
A ZP
A1 D + e+ + e Z
Example:
12 7N
12 C + e+ + e 6
Note : If masses MP , MD and me are given in atomic masses.
A ZP
A1 D + e+ + e Z
(MP Zme )c2 = (MD (Z 1)me )c2 + me c2 + Q Q = (MP MD 2me )c2 When, MP MD 2me + decay occurs.
+ decay scheme 15 O is shown in the gure on the left, and the energy spectrum 8 spectrum for e+ from the decay 64 Cu is shown on the right.
Figure 6: + decay
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Electron Capture
The process of capturing an atomic electron ( usually from K -shell) by the nucleus and emitting a neutrino, is called electron capture. In an electron capture, atomic number of the parent is decreased by one. e +A P A1 D + Z Z Example: e +7 Be 7 Li + 4 3
( i.e. e + p n + ) From the conservation of energy, (Mp + me EK )c2 = MD c2 + Q Q = (Mp + me EK MD )c2 Where EK is the binding energy of the K -shell electron. Q > 0, when (Mp MD ) > EK i.e. Electron capture is only possible when (Mp MD ) > EK . Electron capture produces two particles, daughter and the neutrino, moving in opposite directions with equal momentum. Since the daughter nucleus is heavy, the neutrino carries all of the kinetic energy.
The following gure shows the decay scheme diagram for 22 N a. 10% of the decay occurs through electron capture and the other 90% occurs through the decay.
Decay
The process in which a nucleus initially in an excited state makes a transition to a lower energy state by emitting a photon is called gamma decay.
A ZP
=
A ZP
+
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Figure 7: Electron Capture process
Figure 8: Electron Capture The charge and the atomic number do not change in gamma decay. The energy of the emitted photon is; h = Eu El In most cases, the excited state nucleus is the daughter nucleus following a radioactive decay ( decay or decay) of another nucleus. Most excited nuclei have very short half lives ( 1014 s). The half lives of some nuclei are measurable and seem almost stable. The nucleus in an excited state appears like a separate isotope with same Z and A as the stable nucleus, with more energy. This nucleus is called isomer and its life 12
time is less than 106 s. The transition to the ground state of this nucleus is called the isomeric transition. The excited state is called the metastable state to distinguish from the ground state. In the following decay scheme, 137m Ba from decay of 137 Cs, is a metastable state. 56 55 It decays to the ground state, 137 Ba with a half life of 2.55 s. 56
Figure 9: gamma decay
Internal Conversion
The process in which the energy of the excited state is transferred to an atomic electron ( K or L shell electron) and ejecting it from the atom is called Internal Conversion. The excited state of nucleus may lose its energy by the emission of a gamma ray. This gamma ray can interact with an electron in K -shell. This process perturbs the nucleus and it can transit to the ground state. The energy transfer to the electron,
Ee = E EB
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where EB is the binding energy of the K or L shell electron. The gure shows spectrum of 198 Au with discrete electron energies of 0.329 M eV and 0.403 M eV lines. These electrons come from the internal conversion of 0.412 M eV gamma ray in the K, L + M shells.
Figure 10: Internal Conversion Internal conversion is schematically depicted in the following gure. The nucleus ejects a ray creating a daughter of Z + 1 protons and N 1 neutrons. If the daughter is in an excited state, it can emit a gamma ray E . It can eject a electron in a K -shell with a energy (E EK ) . This creates a hole in the daughter atom.
Figure 11: Internal Conversion The probability of a K -electron conversion is given by the internal conversion yield, 14
K , and it is dened by, K = Number of conversion electrons in K-shell Number of -rays detected
K values range from 0 to 100 or more and increase with increasing Z and decrease with increasing E .
Auger Electrons
The high speed electron, electron capture or internal conversion can create a hole in the K , L or M shell of an atom. This hole can be lled by an electron from an outer shell with an emission of characteristic radiation. In some cases, this characteristic radiation (photon) is absent and in its place, a mono-energetic electron is ejected from the atom. This ejected electron is known as the Auger Electron. Assume a hole was created in the K -shell. An electron from L shell can transit to ll the K -shell. The amount of energy released = EK EL . As an alternative to photon transmission, this energy is transfered to M electron or other ejecting it. Then, where TM + EM = EK EL T = kinetic energy, Ex = Binding energies TM = (EK EL ) EM This process is illustrated in the following gure, and the electron is called the KLM Auger electron
Now the atom has two vacancies, one in L - shell and other in M - shell.
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Figure 12: Auger Electron If two N - shell electrons move in to ll those vacancies the atom emits two more Auger electrons. Assume they are from N - shell, then, we would have four N - shell vacancies. TN1 + EN = EL EN = TN1 = EL 2EN and TN2 + EN = EM EN = TN2 = EM 2EN The total energy of three Auger electrons, TM + TN1 + TN2 = (EK EL ) EM + EL 2EN + EM 2EN TM + TN1 + TN2 = EK 4EN This process repeats, increasing the number of electron vacancies by one for each Auger electron event, until all the vacancies are located in the outer shell. Then, we can show, the total energy carried away by all Auger electrons = EK - (sum of binding energies of all nal electron vacancies) For KLM Auger electrons, we have four vacancies in N -shell. The relative probability of the emission of characteristic radiation to the emission of an Auger electron is called the uorescent yield. Fluorescent yield, K = Number of K , X - ray photons emitted Number of K -shell vacancies 16