© The scientific sentence. 2010
α-decay of radium Ra(226,88)
The basic process is:
X(A,Z) = X(A-4,Z-2) + He(4,2)
1. α-decay process
The nuclide Ra(226,88) decays by alpha exission to
The speed of the emitted α particle is determined experimentally
(the curvature if its path in a transverse magnetic field), or evaluated
by determinig the related mass defect. It is about 1.52 x 107 m/s
( 5% c). We can then use the non-relativistic kinetic energy expression:
KE =(1/2)mv2 = (1/2) (6.64 x 10-27 kg)x (1.52 x 107 m/s) =
The kinetic energy of the emitted α particle
is definite equal to 4.87 MeV. Because of
their mass and charge, they travel only some centimeters
in air and through solids before they get stopped by collisions.
The NEUTRAL atomic mass of the nuclide
Radium(226,88) = 226.025403 u.
The neutral atomic mass of Radon Rn(222,86) = 222.017571 u
The mass of the neutral Helium-4 = 4.002603 u
The difference in mass between the orinal
nucleus Radium(226,88) and the decay final product
Rn(222,86) and He(4,2), called the mass defect is
Δm = 226.025403 u - (222.017571 u + 4.002603 u ) =
0.005229 u . This mass defect is positive, then this
α-decay process is energetically possible.
2. Energy of the emitted α-decay
According to mass-energy equivalence relationship,
we have the corresponding energy is:
ΔE = Δm c2 = Δm (931.5 MeV/u) =
4.87 MeV, which is the binding energy
Note that the momentum of the system ( parent Radium,
daughter Radon, and α particle) is also conserved:
P [Ra] = P[Rn (still doesn't exist)] =
P[&a;pha; (still doesn't exist)] = 0
P[Ra] = 0 , remaining at rest.
P[Rn] = m(Rn) Vrn
P[α] = m(α)vα
The cnosevation of the momentum gives:
0 = P [Ra] + P [Rn] . Therefore:
m(Rn)Vrn = m(α)vα, hence:
Vrn = m(α)vα/m(Rn) = (4.002603/222.017571) vα
= 0.018 vα or 2% vα.
23. Related emitted photon
More precisely, there is intermediate decay during
the α-decay process. The radon produced is at first
in an excited state Rn*(222,86) at an energy
Ei = 0.186 MeV above the ground level.
From this excited level, the Rn* becomes Rn*
by emitting a γ photon of energy 0.186 MeV.