There are actually three types of beta decay. The first discovered was “ordinary” beta decay and is called β−β− size 12{β rSup { size 8{  {}} } } {} decay or electron emission. The symbol β−β− size 12{β rSup { size 8{  {}} } } {} represents an electron emitted in nuclear beta decay. Cobalt60 is a nuclide that β−β− size 12{β rSup { size 8{  {}} } } {} decays in the following manner:
60Co→60Ni+β−+ neutrino.60Co→60Ni+β−+ neutrino. size 12{"" lSup { size 8{"60"} } "Co" rightarrow "" lSup { size 8{"60"} } "Ni"+β rSup { size 8{{}} } +" neutrino"} {}
(9)The neutrino is a particle emitted in beta decay that was unanticipated and is of fundamental importance. The neutrino was not even proposed in theory until more than 20 years after beta decay was known to involve electron emissions. Neutrinos are so difficult to detect that the first direct evidence of them was not obtained until 1953. Neutrinos are nearly massless, have no charge, and do not interact with nucleons via the strong nuclear force. Traveling approximately at the speed of light, they have little time to affect any nucleus they encounter. This is, owing to the fact that they have no charge (and they are not EM waves), they do not interact through the EM force. They do interact via the relatively weak and very short range weak nuclear force. Consequently, neutrinos escape almost any detector and penetrate almost any shielding. However, neutrinos do carry energy, angular momentum (they are fermions with halfintegral spin), and linear momentum away from a beta decay. When accurate measurements of beta decay were made, it became apparent that energy, angular momentum, and linear momentum were not accounted for by the daughter nucleus and electron alone. Either a previously unsuspected particle was carrying them away, or three conservation laws were being violated. Wolfgang Pauli made a formal proposal for the existence of neutrinos in 1930. The Italianborn American physicist Enrico Fermi (1901–1954) gave neutrinos their name, meaning little neutral ones, when he developed a sophisticated theory of beta decay (see Figure 3). Part of Fermi’s theory was the identification of the weak nuclear force as being distinct from the strong nuclear force and in fact responsible for beta decay.
The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. So electrons are given an electron family number of +1+1. The neutrino in β−β− size 12{β rSup { size 8{  {}} } } {} decay is an electron’s antineutrino, given the symbol ν¯eν¯e, where νν is the Greek letter nu, and the subscript e means this neutrino is related to the electron. The bar indicates this is a particle of antimatter. (All particles have antimatter counterparts that are nearly identical except that they have the opposite charge. Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space.) The electron’s antineutrino ν¯eν¯e, being antimatter, has an electron family number of –1–1. The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the total electron family number is constant. An electron cannot be created without also creating an antimatter family member. This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.
If a nuclide ZAXNZAXN is known to β−β− decay, then its β−β− decay equation is
Z
A
X
N
→
Z
+
1
A
Y
N
−
1
+
β
−
+
ν

e
(
β
−
decay
)
,
Z
A
X
N
→
Z
+
1
A
Y
N
−
1
+
β
−
+
ν

e
(
β
−
decay
)
,
size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z+1} } lSup { size 8{A} } Y rSub { size 8{N  1} } +β rSup { size 8{  {}} } + { bar {ν}} rSub { size 8{e} } ``` \( β rSup { size 8{  {}} } `"decay" \) ,} {}
(10)where Y is the nuclide having one more proton than X (see Figure 4). So if you know that a certain nuclide β−β− decays, you can find the daughter nucleus by first looking up
ZZ for the parent and then determining which element has atomic number
Z+1Z+1. In the example of the
β−β− decay of
60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {} given earlier, we see that Z=27Z=27 for Co and
Z=28Z=28 is Ni. It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. In fact, neutrons outside of nuclei do just that—they live only an average of a few minutes and
β−β− decay in the following manner:
n
→
p
+
β
−
+
ν

e
.
n
→
p
+
β
−
+
ν

e
.
size 12{n rightarrow p+β rSup { size 8{  {}} } + { bar {ν}} rSub { size 8{e} } } {}
(11)We see that charge is conserved in β−β− decay, since the total charge is ZZ size 12{Z} {} before and after the decay. For example, in 60Co60Co decay, total charge is 27 before decay, since cobalt has
Z=27Z=27. After decay, the daughter nucleus is Ni, which has
Z=28Z=28, and there is an electron, so that the total charge is also 28 + (–1)28 + (–1) or 27. Angular momentum is conserved, but not obviously (you have to examine the spins and angular momenta of the final products in detail to verify this). Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. The total number of nucleons AA is conserved. In
60Co60Co decay, for example, there are 60 nucleons before and after the decay. Note that total
AA is also conserved in
αα decay. Also note that the total number of protons changes, as does the total number of neutrons, so that total
ZZ size 12{Z} {} and total NN size 12{N} {} are not conserved in β−β− size 12{β rSup { size 8{  {}} } } {} decay, as they are in αα size 12{α} {} decay. Energy released in β−β− size 12{β rSup { size 8{  {}} } } {} decay can be calculated given the masses of the parent and products.
Find the energy emitted in the β−β− size 12{β rSup { size 8{  {}} } } {} decay of 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {}.
Strategy and Concept
As in the preceding example, we must first find ΔmΔm, the difference in mass between the parent nucleus and the products of the decay, using masses given in Appendix A. Then the emitted energy is calculated as before, using E=(Δm)c2E=(Δm)c2. The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. However, since the masses given in Appendix A are for neutral atoms, the daughter nucleus has one more electron than the parent, and so the extra electron mass that corresponds to the β–β– is included in the atomic mass of Ni. Thus,
Δm=m(60Co
)−m(60Ni).Δm=m(60Co
)−m(60Ni). size 12{Δm=m \( "" lSup { size 8{"60"} } "Co" \) m \( "" lSup { size 8{"60"} } "Ni" \) } {}
(12)
Solution
The β−β− decay equation for 60Co60Co size 12{"" lSup { size 8{"60"} } "Co"} {} is
2760Co33
→
2860Ni32
+
β
−
+ν¯e.2760Co33
→
2860Ni32
+
β
−
+ν¯e.
(13)As noticed,
Δm=m(60Co
)−m(60Ni).Δm=m(60Co
)−m(60Ni). size 12{Δm=m \( "" lSup { size 8{"60"} } "Co" \) m \( "" lSup { size 8{"60"} } "Ni" \) } {}
(14)Entering the masses found in Appendix A gives
Δm=59.933820 u−59.930789 u=0.003031 u.Δm=59.933820 u−59.930789 u=0.003031 u.
(15)Thus,
E=(Δm)c2=(0.003031 u)c2.E=(Δm)c2=(0.003031 u)c2. size 12{E= \( Δm \) c rSup { size 8{2} } = \( 0 "." "003031" \) \( uc rSup { size 8{2} } \) } {}
(16)Using 1 u=931.5 MeV/c21 u=931.5 MeV/c2, we obtain
E=(0.003031)(931.5 MeV/c2)(c2)=2.82 MeV.E=(0.003031)(931.5 MeV/c2)(c2)=2.82 MeV. size 12{E= \( 0 "." "003031" \) \( "931" "." 5" MeV"/c rSup { size 8{2} } \) \( c rSup { size 8{2} } \) =2 "." "82"" MeV"} {}
(17)
Discussion and Implications
Perhaps the most difficult thing about this example is convincing yourself that the β−β− size 12{β rSup { size 8{  {}} } } {} mass is included in the atomic mass of 60Ni60Ni. Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay. In many 60Co60Co decays, the daughter nucleus 60Ni60Ni is left in an excited state and emits photons (
γγ size 12{g} {} rays). Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. One final note: the electron emitted in β−β− decay is created in the nucleus at the time of decay.
The second type of beta decay is less common than the first. It is β+β+ size 12{β rSup { size 8{+{}} } } {}decay. Certain nuclides decay by the emission of a positive electron. This is antielectron or positron decay (see Figure 5).
The antielectron is often represented by the symbol e+e+ size 12{e rSup { size 8{+{}} } } {}, but in beta decay it is written as β+β+ size 12{β rSup { size 8{+{}} } } {} to indicate the antielectron was emitted in a nuclear decay. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of –1–1. When a positron encounters an electron, there is a mutual annihilation in which all the mass of the antielectronelectron pair is converted into pure photon energy. (The reaction, e++e−→γ+γe++e−→γ+γ size 12{e rSup { size 8{+{}} } +e rSup { size 8{{}} } rightarrow g+g} {}, conserves electron family number as well as all other conserved quantities.) If a nuclide ZAXNZAXN is known to β+β+ decay, then its β+β+ size 12{β rSup { size 8{+{}} } } {}decay equation is
ZA
X
N
→
Z
−
1
A
Y
N
+
1
+
β
+
+
ν
e
(
β
+
decay
)
,
ZA
X
N
→
Z
−
1
A
Y
N
+
1
+
β
+
+
ν
e
(
β
+
decay
)
,
size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z  1} } lSup { size 8{A} } Y rSub { size 8{N+1} } +β rSup { size 8{+{}} } +ν rSub { size 8{e} } ```` \( β rSup { size 8{+{}} } `"decay" \) ,} {}
(18)where Y is the nuclide having one less proton than X (to conserve charge) and νeνe is the symbol for the electron’s neutrino, which has an electron family number of +1+1. Since an antimatter member of the electron family (the β+β+) is created in the decay, a matter member of the family (here the νeνe) must also be created. Given, for example, that
22Na22Na
β+β+ size 12{β rSup { size 8{+{}} } } {} decays, you can write its full decay equation by first finding that Z=11Z=11 for 22Na22Na, so that the daughter nuclide will have
Z=10Z=10 size 12{Z="10"} {}, the atomic number for neon. Thus the β+β+ size 12{β rSup { size 8{+{}} } } {} decay equation for 22Na22Na is
1122Na11→1022Ne12+β++νe.1122Na11→1022Ne12+β++νe.
(19)In β+β+ size 12{β rSup { size 8{+{}} } } {} decay, it is as if one of the protons in the parent nucleus decays into a neutron, a positron, and a neutrino. Protons do not do this outside of the nucleus, and so the decay is due to the complexities of the nuclear force. Note again that the total number of nucleons is constant in this and any other reaction. To find the energy emitted in β+β+ size 12{β rSup { size 8{+{}} } } {} decay, you must again count the number of electrons in the neutral atoms, since atomic masses are used. The daughter has one less electron than the parent, and one electron mass is created in the decay. Thus, in β+β+ size 12{β rSup { size 8{+{}} } } {} decay,
Δm=m(parent)−[m(daughter)+2me],Δm=m(parent)−[m(daughter)+2me],
(20)since we use the masses of neutral atoms.
Electron capture is the third type of beta decay. Here, a nucleus captures an innershell electron and undergoes a nuclear reaction that has the same effect as β+β+ size 12{β rSup { size 8{+{}} } } {} decay. Electron capture is sometimes denoted by the letters EC. We know that electrons cannot reside in the nucleus, but this is a nuclear reaction that consumes the electron and occurs spontaneously only when the products have less mass than the parent plus the electron. If a nuclide ZAXNZAXN is known to undergo electron capture, then its electron capture equation is
ZA
X
N
+
e
−
→
Z
−
1
A
Y
N
+
1
+
ν
e
(
electron capture, or EC
)
.
ZA
X
N
+
e
−
→
Z
−
1
A
Y
N
+
1
+
ν
e
(
electron capture, or EC
)
.
size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } +e rSup { size 8{  {}} } rightarrow "" lSub { size 8{Z  1} } lSup { size 8{A} } Y rSub { size 8{N+1} } +ν rSub { size 8{e} } ``` \( "electron capture, or EC" \) "." } {}
(21)Any nuclide that can β+β+ size 12{β rSup { size 8{+{}} } } {} decay can also undergo electron capture (and often does both). The same conservation laws are obeyed for EC as for β+β+ size 12{β rSup { size 8{+{}} } } {} decay. It is good practice to confirm these for yourself.
All forms of beta decay occur because the parent nuclide is unstable and lies outside the region of stability in the chart of nuclides. Those nuclides that have relatively more neutrons than those in the region of stability will β−β− size 12{β rSup { size 8{  {}} } } {} decay to produce a daughter with fewer neutrons, producing a daughter nearer the region of stability. Similarly, those nuclides having relatively more protons than those in the region of stability will β−β− size 12{β rSup { size 8{  {}} } } {} decay or undergo electron capture to produce a daughter with fewer protons, nearer the region of stability.
"This introductory, algebrabased, twosemester college physics book is grounded with realworld examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. […]"