Physics and Engineering of Radiation Detection

626 Chapter 11. Dosimetry and Radiation Protection

table 11.2.5. To compute the energy released, one must first write the equation for
the capture reaction and then calculate theQ-value using energy conservation (see
example below).

Table 11.2.5: Percentage by mass, atom densities and capture cross sections of
elements in a typical soft tissue.

Element Percentage (by mass) ρa(cm−^3 ) σc(barn)

Oxygen 76.2% 2. 45 × 1022 1. 9 × 10 −^4

Carbon 11.1% 9. 03 × 1021 3. 5 × 10 −^3

Hydrogen 10.1% 5. 98 × 1022 0.33

Nitrogen 2.6% 1. 29 × 1021 1.70

Example:

Compute the energy released after the capture of a thermal neutron by

nitrogen-14 at rest.

Solution:

The capture reaction can be written as

14

7 N+n→

14

6 C+p.

Conservation of energy implies that

m 0 , 1 c^2 +m 0 ,nc^2 =m 0 , 2 c^2 +mp, 2 c^2 +Ep,

wherem 0 , 1 andm 0 , 2 represent therest masses of nitrogen and carbon re-

spectively.m 0 ,nandm 0 ,pare the rest masses of the neutron and the proton

respectively. Eprepresents the kinetic energy of the released proton. Note

that here we have ignored the kinetic energies of all particle, except of course

of the released proton. The reason is that the nitrogen and carbon are bound

in the bulk mass of the tissue by chemical bonds and therefore their kinetic

energies (mostly vibrational) are very small compared to their rest energies.

The thermal neutron on the other hand, though moving, has a kinetic energy

insignificantly smaller as compared to its rest energy.

The energy released is therefore given by

Ep =(m 0 , 1 +m 0 ,n−m 0 , 2 −m 0 ,p)c^2 J

⇒Ep =(m 0 , 1 +m 0 ,n−m 0 , 2 −m 0 ,p) 931. 48 MeV,

where the masses in the first equation are inkgwhile in the second are in

amu. The second equation is much more convenient to use since it gives the