Figure 4-3. Radium-226 transformation (de-cay) scheme.
of the alpha particles. Radium may be cited as an example of an alpha emitter with a complex spectrum (Fig. 4-3). In the overwhelming majority of transformations of
226Ra (94.3%), alphas are emitted with a kinetic energy of 4.777 MeV. The remain-ing alpha particles (5.7%) have kinetic energies of only 4.591 MeV. In that instance, where a lower energy alpha is emitted, the daughter nucleus is left in an excited state and rids itself of its energy of excitation by emitting a gamma-ray photon whose energy is equal to the difference between the energies of the two alpha particles:
4.777−4.591=0.186 MeV. (About 35% of these gamma-ray photons are internally converted: see the section on “Internal Conversion.”) The226Ra spectrum is among the least intricate of all the complex alpha spectra. Most alpha emitters have several groups of alphas and therefore more gammas. All alpha spectra, however, show the same consistent relationship among the various nuclear energy levels.
Alpha particles are extremely limited in their ability to penetrate matter. The dead outer layer of skin is sufficiently thick to absorb all alpha radiations from radioactive materials. As a consequence, alpha radiation from sources outside the body does not constitute a radiation hazard. In the case of internally deposited alpha-emitting radionuclides, however, the shielding effect of the dead outer layer of skin is absent and the energy of the alpha radiation is dissipated in living tissue. For this reason and others to be discussed in Chapter 7, alpha radiation is a concern when it irradiates the inside of the body from internally deposited radioisotopes.
Isobaric Transitions
This transformation shows that beta decay occurs among those nuclides that have a surplus of neutrons. For beta emission to be energetically possible, the exact nuclear mass of the parent must be greater than the sum of the exact masses of the daughter nucleus plus the beta particle.
Mp=Md+Me+Q. (4.7)
This restriction, of course, is analogous to the corresponding restriction on alpha emitters. Because a unit negative charge is lost during beta decay and the mass of the beta particle is1 amu, the daughter nucleus is one atomic number higher than its parent but retains the same atomic mass number as the parent. For example, radioactive phosphorus decays to stable sulfur according to the equation
32
15P→3216S+−01e+1.71 MeV.
The transformation energy, in this instance 1.71 MeV, is the energy equivalent of the difference in mass between the 32P nucleus and the sum of the masses of the
32S nucleus and the beta particle, and appears as kinetic energy of the beta particle.
If neutral atomic masses are used to complete the mass–energy equation, then, of course, the mass of the electron shown in the right-hand side of Eq. (4.7) is not considered since it is implicitly included in the extranuclear electronic structure of the32S. The mass difference is
31.973907=31.972070+Q Q =0.001837 amu
and the energy equivalent of the mass difference is 0.001837×931 MeV/amu=1.71 MeV.
Examination of Eq. (4.5) shows that in the case of beta emission, an extremely small part of the energy of the reaction is dissipated by the recoil nucleus sincem/M (wherem is now the mass of the beta particle and M is the mass of the daughter nucleus) is very small. In the example given above,
m
M =0.00055
32 =0.000017
andQ is only 1.000017 times greater than the kinetic energy of the beta particle.
On the basis of the above analysis, one might expect beta particles to be mo-noenergetic, as in the case of alpha radiation. This expectation is not confirmed by experiment. Instead, beta particles are found to be emitted with a continuous energy distribution ranging from zero to the theoretically expected value based on mass–energy considerations for the particular beta transition. In the case of32P, for example, although the maximum energy of the beta particle may be 1.71 MeV, most of the betas have considerably smaller kinetic energies, as shown in Figure 4-4. The average energy of a32P beta particle is 0.7 MeV or about 41% of the maximum en-ergy. Generally, the average energy of the beta radiation from the most beta-active
Figure 4-4. Phosphorous-32 beta spectrum.
radioisotopes is about 30–40% of the maximum energy. Unless otherwise specified, whenever the energy of a beta emitter is given, it implies the maximum energy.
The fact that beta radiation is emitted with a continuous energy distribution up to a definite maximum seems to violate the established energy–mass conservation laws.
This is explained by the simultaneous emission of a second type of particle, called a neutrino,1whose energy is equal to the difference between the kinetic energy of the accompanying beta particle and the maximum energy of the spectral distribution.
The neutrino, as postulated, has no electrical charge and a vanishingly small mass.
Although these two characteristics make detection of the neutrino difficult, neu-trinos have been measured and the neutrino hypothesis has been experimentally verified. Equation (4.6) should therefore be modified to
1
0n→11H +−01e +ν, (4.8)
whereνrepresents the neutrino.
Phosphorus-32, like several other beta emitters—including 3H, 14C, 90Sr, and
90Y—emits no gamma rays. These isotopes are known as pure beta emitters. The opposite of a pure beta emitter is a beta–gamma emitter. In this case, the beta particle is followed instantaneously (in most cases) by a gamma ray. For those ra-dionuclides where the gamma-ray emission is delayed, as in the case of99mTc and
137Cs, the gamma-ray emission is called an isomeric transition.In an isomeric tran-sition, the atomic number and the atomic mass number of the radionuclide is not changed. The explanation for the gamma ray here is the same as that in the case of the alpha. The daughter nucleus, after the emission of a beta, is left in an excited condition and rids itself of the energy of excitation by the emission of a gamma ray. Mercury-203 may be given as an example. It emits a 0.21-MeV beta and a 0.279-MeV gamma, as seen in the transformation scheme shown in Figure 4-5.
Both illustrations given above (32P and203Hg) are for beta emitters with simple spectra, that is, for emitters with only one group of beta particles. Complex beta emit-ters are those radionuclides whose beta spectra contain more than one distinct group
1Technically this is an antineutrino, but in common parlance, unless there is a need to be more specific, this particle is referred to as a neutrino.
203Hg
203TI 0
0.279
γ, 0.279 MeV (17%ε−)
Figure 4-5. Transformation (decay) scheme of203Hg.
of beta particles. Potassium-42, for example, in about 82% of its transformations, de-cays to stable42Ca by emission of a beta particle from a group whose maximum energy is 3.55 MeV and in 18% of its transformations by emitting a 2.04-MeV beta particle (Fig. 4-6). In this case, however, the excited 42Ca immediately emits a gamma-ray whose energy is 1.53 MeV. A commonly used radionuclide that has an even more complex beta–gamma spectrum is131I. This isotope decays to stable131Xe by emis-sion of a beta particle. In 90.4% of the transformations, however, the beta particle is a member of a group whose maximum energy is 0.61 MeV, while the remaining beta particles belong to groups whose maximum energies range from 0.81 MeV in 0.6%
of the transformations to 0.25 MeV in 1.6% of the transformations. In all instances, each xenon daughter nucleus is left in an excited state and rids itself of its excita-tion energy by the emission of gamma radiaexcita-tion. The nucleus resulting from the emission of the 0.61-MeV beta particle rids itself of its excitation energy by two com-peting gamma-ray transitions. About 94% of these nuclei (corresponding to 85.3%
of the131I transformations) emit 0.364-MeV gamma rays, and the remaining excited nuclei emit two gamma rays in cascade—one of 0.284 MeV and one of 0.080 MeV.
The transformation scheme for131I is shown in Figure 4-7.
42K
42Ca
β-, 2.04 MeV (18%) β-, 3.55 MeV
(82%)
γ, 1.53 MeV
Figure 4-6. Potassium-42 transformation (decay) scheme.
Figure 4-7. Iodine-131 transformation (decay) scheme.
Beta radiation, because of its ability to penetrate tissue to varying depths, depend-ing on the energy of the beta particle, may be an external radiation hazard. The exact degree of hazard, of course, depends on the beta energy and must be evaluated in every case. Generally, however, beta particles whose energies are less than 200 keV have very limited penetrability. Examples of these include3H,35S, and14C. None of these are considered as external radiation hazards. It should be noted, however, that beta particles give rise to highly penetrating X-rays calledbremsstrahlungwhen they strike a high-atomic-numbered absorbing material. (This interaction is more fully discussed later, in Chapter 5.) Unless shielding is appropriately designed and proper precautionary measures are adopted, beta radiation may indirectly result in an ex-ternal radiation hazard through the production of bremsstrahlung radiation. Any beta-emitting radionuclide, of course, is potentially hazardous when it is deposited in the body in amounts exceeding those thought to be safe.