Physics and Engineering of Radiation Detection

1.3. Radioactivity and Radioactive Decay 9

of electronic transitions between atomic levels. The particles that are not emitted
from the nucleus can be byproducts of a decay but should not be confused with the
direct decay products.

Example:

Write down equations for alpha decay of Thorium-232 and electron decay of

Sodium-24.

Solution:

Using the general decay equations defined above and the periodic table of

elements we find the required decay equations.

232

90 Th →

228

88 Ra+α

24

11 Na →

24

12 Mg+e+ ̄ν

1.3.A Decay Energy orQ-Value

Decay energy is a term used to quantify the energy released during the decay process.
It can be used to determine whether a certain decay mode for a nucleus is possible
or not. To understand this, let us suppose a nucleusXgoes through a decay mode
that transforms it into a nucleusY with a subsequent emission of a particled.This
reaction can be written as
X→Y+d. (1.3.1)

According to the law of conservation of energy, the total energy before and after the
decay should be equal, that is

E 0 ,X+TX=E 0 ,Y+TY+E 0 ,d+Td, (1.3.2)

whereE 0 stands for the rest energy andTrepresents the kinetic energy. The rest
energy can be computed from the Einstein relationE 0 =m 0 c^2 ,withm 0 being the
rest mass. Since the decaying nucleusXcanbeassumedtobeatrestthereforewe
can safely useTX= 0 in the above relation. If we represent the rest masses ofX
andYbymXandmY, the above equation would read

(mX−mY−md)c^2 =TY+Td. (1.3.3)

Now, it is evident that the left hand side of this relation must be positive in order for
the kinetic energy to be positive and meaningful. In other words, the decay would
be possible only if the left hand side is positive valued. Both the left and right hand
sides of this relation are termed as the decay energy or theQ-value. That is

Qd = TY+Td (1.3.4)

or Qd =(mX−mY−md)c^2. (1.3.5)

The first relation above requires the knowledge of the kinetic energy taken away
by the decaying nucleus and the emitted particle. These energies are difficult to
determine experimentally, though. Therefore, generally one uses the second relation
containing the mass terms to determine the decay energy for any decay mode the