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Examples of Decay Scheme Examples Problems Chapter 3 Radiation Protection Book Problem #1 137 55Cs decays by beta- emission (T=30.174y, Δ = -86.5607 MeV) to 137 56Ba (Δ = -87.7367 MeV) with the emission of the following radiations: β- : 1.176 Mev; max 7% 0.514 Mev; max 93% γ: 0.662 MeV; 85% Problem # 1 Questions 137 (a) draw the decay scheme of 55Cs Calculate the conversion coefficient Calculate the K-shell conversion- electron energy if the K-shell binding energy is 37 keV What is Auger electron emission and with what process does it compete? Problem #1: Solution 137 137 0 0 Cs55 →56 Ba +−1β 0 + v =Q Δp − D Δ Q86= −. 5607(MeV 87− −. 7367MeV ) 1Q = . 176MeV Problem #1: Solution This agrees with the larger of the 2 observed maximum beta-particle energies This indicates that 7% of the parent nuclei decay directly to the ground state of the daughter The remaining 93% decay to a daughter excited state, having an energy of: − = 662.0514.0176.1 MeV – The observed gamma-ray energy Problem #1: Solution The gamma-ray is observed in only 85% of the transformations So, internal conversion must occur in – 93% - 85% = 8% of the transformations Decay scheme drawing 137 55Cs 1.176 MeV Beta: 0.512 (93%) Beta = 1.176 (7%) 0.662 MeV Gamma (85%) 0 MeV 137 56Ba X-rays from daughter will also occur as a result of rearrangements of orbital electrons following internal conversion They are not shown in decay scheme diagrams, which show only nuclear transformation Internal conversion Occurs when nuclear de-excitation causes ejection of an electron from an atomic shell as an alternative to gamma emission It is favored over gamma emission in elements of low Z and low energy transitions K and L-shell electrons are most likely to be involved due to their close proximity to the nucleus Internal conversion The conversion coefficient : N α = e Nγ 0 . 08 α=0 . = 094 0 . 85 K-shell electron energy In contrast to a beta particle, a conversion electron has a discrete energy equal to the difference between the gamma-ray energy and the electron’s binding energy: EEEe = *− B 0 . 662 0− . 037= M 0eV . 625 Conversion electrons from other shells have higher energies since their binding energy is lower, but occur less frequently Note that since the conversion electron is emitted from the daughter atom, the binding energy of the daughter, not parent, determines the energy of the conversion electron Auger electron An auger electron is emitted instead of a characteristic X-ray when the energy released is transformed to another atomic electron, removing it from the atom Auger electron emission is the atomic analog to internal conversion Since both electron capture and internal conversion leave a vacancy in an orbital electron shell, both can give rise to Auger electron emission The number of X-rays emitted per vacancy is called the fluorescence yield and is equal to 1 for high Z elements Problem #2 59 26Fe emits beta particles via four modes of decay with the maximum energies and frequencies shown in Table. It also emits gamma photons as indicated Radiations emitted by 5 26Fe Beta Particles Photons Max. Energy Frequency Energy Frequency [MeV] [%] [MeV] [%] 1.573 0.3 1.290 43.4 0.475 53.5 1.098 56.3 0.283 45.4 0.192 2.8 0.140 0.8 0.143 0.8 Solution To develop a decay scheme from a list of radiations emitted, fit one piece of information at a time The frequencies for beta decay add to 100% The average number of gamma-rays per transformation exceeds one Multiple photons will thus be emitted in some modes of decay Beta decay to the ground The simplest assumption is that the most energetic mode of beta decay 59 (Q=1.573) leaves the daughter 27Co nucleus in its ground state 59 1.573 26Fe 1.573 0.3% 59 0.0 27Co The 4 modes of beta decay The other modes of beta decay leave the 59 27Co in nucleus excited states with energies: 1 . 573 0− . 475= MeV 1 . 098 1 . 573 0− . 283 = MeV 1 . 290 1 . 573 0− . 140 = MeV 1 . 433 The 4 modes of beta decay Fe59 1.573 26 0.140 0.8% 0.382 1.433 45.4% 0.475 53.5% 1.290 1.573 0.3% 1.098 59 0.0 27Co Gamma-decay If the daughter nucleus is left in one of the excited states after emission of the beta particle, then it decays to the ground state by emitting one or more gamma photons The energies of the photons 1 . 433 1− . 290= MeV 0 . 143 1 . 433 1− . 098 = MeV 0 . 335 1 . 433− 0 . 0 = 1MeV . 433 1 . 290 1− . 098 = MeV 0 . 192 1 . 290− 0 . 0 = 1MeV . 290 1 . 098− 0 . 0 = 1MeV . 098 Complete Decay-Scheme Fe59 1.573 26 0.140 0.8% 0.382 1.433 45.4% 0.143 0.475 0.8% 53.5% 1.290 1.573 0.3% 0.192 2.8% 1.098 1.290 1.098 43.4% 56.3% 59 0.0 27Co.
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