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 
Radon Rn(222,86).
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) = 
4.87 MeV.
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:

Before decaying:
P [Ra] = P[Rn (still doesn't exist)] = 
P[&a;pha; (still doesn't exist)] = 0

After decaying:
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.