The Recoil Energy of the Nucleus
As has already been noted, the energy released in nuclear processes is much greater than that
involved in most chemical processes. The energy that is released in a nuclear reaction or decay is
divided between the emitted particle or radiation and the nucleus that remains after the emission.
The divission of energy is governed by the law of conversation of momentum, which requires
that the momentum of a γ ray or particle emitted from a nucleus be equal to the momentum of
the nucleus remaining after the decay.
An equation to calculate the recoil energy of the nucleus may be simply derived. Reaction
resulting in γ-ray emission will be discussed first. The energies of the recoil particles (Er) and the
gamma ray (Eγ) can be given as
1
Eγ = mc 2
Er = mr v 2
2
(1)
Rearranging these equation for the particle and the gamma ray gives
Eγ
c
= mc = pγ
2mr(Er ) = (mr v)2 = p2r
(2)
and
2
(pγ ) =
(Eγ )
2
c2
2
(pγ ) = 2mr Er
(3)
By the law of conversation of momentum,
2
(pγ ) = (pr )2
(4)
so
(Eγ )
2
c2
= 2mr Er
(5)
The energy of the recoil species is
Er =
(Eγ )
2
(6)
2mr c2
If energy is given in units of MeV and mass in daltons, Eq.6 becomes
(Eγ,MeV )
Er,MeV = 1862m
2
r,daltons
By using eV as energy units instead of MeV, the equation is
(7)
Er,eV =
537(Eγ,MeV )
2
mr,daltons
(8)
The production of a hot atom by beta decay, electron capture, or internal conversion produces
lower recoil energies, sometimes even lower than the chemical bond energies. The equation used
to calculate recoil energy for beta decay is different from that used for gamma decay :
Erecoil,max =
537Eβ (Eβ +1,02)
mrecoil,daltons
(9)
Where Eβ is in units of MeV and Erecoil,max is in units of eV. This energy would represent the
maximum energy for the beta particle.
References
Ehmann, W.D. and Vance, D.E. 1991. Radiochemistry and Nuclear Methods of Analysis.
Brisbane : John Wiley & Sons, Inc