Examples Problems

Chapter 3Radiation Protection Book

Problem #1

55Cs137 decays by beta- emission (T=30.174y, Δ = -86.5607 MeV) to 56Ba137 (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

(a) draw the decay scheme of 55Cs137

Calculate the conversion coefficientCalculate the K-shell conversion-electron energy if the K-shell binding energy is 37 keVWhat is Auger electron emission and with what process does it compete?

Problem #1: Solution

MeVQMeVMeVQ

QvBaCs

Dp

176.1)7367.87(5607.86

00

01

13756

13755

=−−−=

Δ−Δ=++→ − β

Problem #1: Solution

This agrees with the larger of the 2 observed maximum beta-particle energiesThis indicates that 7% of the parent nuclei decay directly to the ground state of the daughterThe remaining 93% decay to a daughter excited state, having an energy of:

– The observed gamma-ray energy

MeV662.0514.0176.1 =−

Problem #1: Solution

The gamma-ray is observed in only 85% of the transformationsSo, internal conversion must occur in – 93% - 85% = 8% of the transformations

Decay scheme drawing

55Cs137

56Ba137

Gamma (85%)

Beta: 0.512 (93%)Beta = 1.176 (7%)

1.176 MeV

0.662 MeV

0 MeV

X-rays from daughter will also occur as a result of rearrangements of orbital electrons following internal conversionThey 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 emissionIt is favored over gamma emission in elements of low Z and low energy transitionsK and L-shell electrons are most likely to be involved due to their close proximity to the nucleus

Internal conversion

The conversion coefficient :

094.085.008.0

==

=

α

αγN

Ne

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:

Conversion electrons from other shells have higher energies since their binding energy is lower, but occur less frequentlyNote 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

MeVEEE Be

625.0037.0662.0*

=−−=

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 atomAuger electron emission is the atomic analog to internal conversionSince both electron capture and internal conversion leave a vacancy in an orbital electron shell, both can give rise to Auger electron emissionThe number of X-rays emitted per vacancy is called the fluorescence yield and is equal to 1 for high Z elements

Problem #2

26Fe59 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 26Fe5

Max. Energy [MeV]

Frequency[%]

Energy[MeV]

Frequency[%]

1.573 0.3 1.290 43.4

0.475 53.5 1.098 56.30.283 45.4 0.192 2.80.140 0.8 0.143 0.8

Beta Particles Photons

Solution

To develop a decay scheme from a list of radiations emitted, fit one piece of information at a timeThe frequencies for beta decay add to 100%The average number of gamma-rays per transformation exceeds oneMultiple 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 (Q=1.573) leaves the daughter 27Co59

nucleus in its ground state1.573

0.027Co59

26Fe59

1.5730.3%

The 4 modes of beta decay

The other modes of beta decay leave the 27Co59 in nucleus excited states with energies:

MeVMeVMeV

433.1140.0573.1290.1283.0573.1098.1475.0573.1

=−=−=−

The 4 modes of beta decay

1.573

0.027Co59

26Fe59

1.5730.3%

0.47553.5%

0.38245.4%

0.1400.8%

1.433

1.290

1.098

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

MeVMeV

MeVMeV

MeVMeV

098.10.0098.1290.10.0290.1

192.0098.1290.1433.10.0433.1

335.0098.1433.1143.0290.1433.1

=−=−=−

=−=−=−

Complete Decay-Scheme1.573

0.027Co59

26Fe59

1.5730.3%

0.47553.5%

0.38245.4%

0.1400.8%

1.433

1.290

1.098

0.1430.8%

0.1922.8%

1.29043.4%

1.09856.3%