18
2 Radioactivity
22 Na 11 → β
+
+
22 Ne 10
In this example, Sodium-22 has 11 electrons while Neon has only 10 electrons,
which means that the mass of one electron should be considered in the calculation.
It is important to realize that a positron (i.e., β
+ ) has been evolved from the nucleus
due to the conversion of the proton into a neutron and is not due to orbital electrons
of Sodium and Neon.
Mass of Sodium-22
= 21.994435 a.m.u
Mass of Neon-22
= 21.9913845 a.m.u
Mass difference
= 0.0030505 a.m.u
Energy equivalent
= 0.0030505 a.m.u. × 931.5 MeV
= 2.84 MeV
Mass of one electron
= 9.10939 × 10 −31 kg
= 0.511 MeV
because 1 a.m.u.
= 1.66054 × 10 −27 kg
Thus mass of two electrons = 2 × 0.511 MeV, i.e., (e − + e + ) = 1.022 MeV
This calculation suggests that since energy equivalent to mass difference (
22 Na 11 −
22 Ne 10 = 2.84 MeV) is greater than the sum total of electron and positron energies
(e
−
+ e
+
= 1.022 MeV), positron emission is energetically possible. This is also the
case with Sodium-22; it decays by positron emission. On the other hand, decay by
electron capture simply involves the transfer of an orbital electron to the nucleus
(i.e., it is not lost from the system).
Thus, for an electron capture decay, mass of
A X Z -mass of
A Y Z−1 must be greater
than zero. In other words, for electron capture decay, it is only necessary for the atom
A X Z to be heavier than
A Y Z−1 .
The unstable nuclei
55 Fe 26 that decay to
55 Mn 25 by electron capture can be considered as an example to illustrate this phenomenon.
Mass of Iron-55
= 54.9383024 a.m.u
Mass of Manganese-55 = 54.9380536 a.m.u
Mass difference
= 0.0002488 a.m.u
Energy equivalent
= 931.5 × 0.0002488 MeV = 0.231 MeV
Thus, Iron-55 can decay only by electron capture, which is observed in its decay.
Hence as a general rule, it can be remembered that if mass difference of (
A X Z −
A Y Z−1 ) is greater than the energy equivalent to (e
−
+ e
+
) = 1.022 MeV, positron
emission as well as electron capture are possible; but if this energy is less than
1.022 MeV, only electron capture is possible. However, it is observed that among the
lighter elements, positron emission and electron capture are approximately equally
probable, but as the atomic number of nuclei increases, the orbital electrons are
drawn toward the nucleus and the probability of electron capture increases. Positron
emission is not usually observed in heavy elements.
The detection of an isotope decaying by electron capture becomes a difficult task
because excess energy is released in the form of X -rays. Since electron capture occurs
with electrons of the innermost orbital, the vacancy created in this orbit is filled by
2 Radioactivity
22 Na 11 → β
+
+
22 Ne 10
In this example, Sodium-22 has 11 electrons while Neon has only 10 electrons,
which means that the mass of one electron should be considered in the calculation.
It is important to realize that a positron (i.e., β
+ ) has been evolved from the nucleus
due to the conversion of the proton into a neutron and is not due to orbital electrons
of Sodium and Neon.
Mass of Sodium-22
= 21.994435 a.m.u
Mass of Neon-22
= 21.9913845 a.m.u
Mass difference
= 0.0030505 a.m.u
Energy equivalent
= 0.0030505 a.m.u. × 931.5 MeV
= 2.84 MeV
Mass of one electron
= 9.10939 × 10 −31 kg
= 0.511 MeV
because 1 a.m.u.
= 1.66054 × 10 −27 kg
Thus mass of two electrons = 2 × 0.511 MeV, i.e., (e − + e + ) = 1.022 MeV
This calculation suggests that since energy equivalent to mass difference (
22 Na 11 −
22 Ne 10 = 2.84 MeV) is greater than the sum total of electron and positron energies
(e
−
+ e
+
= 1.022 MeV), positron emission is energetically possible. This is also the
case with Sodium-22; it decays by positron emission. On the other hand, decay by
electron capture simply involves the transfer of an orbital electron to the nucleus
(i.e., it is not lost from the system).
Thus, for an electron capture decay, mass of
A X Z -mass of
A Y Z−1 must be greater
than zero. In other words, for electron capture decay, it is only necessary for the atom
A X Z to be heavier than
A Y Z−1 .
The unstable nuclei
55 Fe 26 that decay to
55 Mn 25 by electron capture can be considered as an example to illustrate this phenomenon.
Mass of Iron-55
= 54.9383024 a.m.u
Mass of Manganese-55 = 54.9380536 a.m.u
Mass difference
= 0.0002488 a.m.u
Energy equivalent
= 931.5 × 0.0002488 MeV = 0.231 MeV
Thus, Iron-55 can decay only by electron capture, which is observed in its decay.
Hence as a general rule, it can be remembered that if mass difference of (
A X Z −
A Y Z−1 ) is greater than the energy equivalent to (e
−
+ e
+
) = 1.022 MeV, positron
emission as well as electron capture are possible; but if this energy is less than
1.022 MeV, only electron capture is possible. However, it is observed that among the
lighter elements, positron emission and electron capture are approximately equally
probable, but as the atomic number of nuclei increases, the orbital electrons are
drawn toward the nucleus and the probability of electron capture increases. Positron
emission is not usually observed in heavy elements.
The detection of an isotope decaying by electron capture becomes a difficult task
because excess energy is released in the form of X -rays. Since electron capture occurs
with electrons of the innermost orbital, the vacancy created in this orbit is filled by