Physics and Engineering of Radiation Detection

12.1. Spectroscopy of Photons 681

NEXAFS EXAFS

X−ray Energy

X−ray Intensity

Figure 12.1.7: Typical x-ray

absorption spectrum. The spec-

trum is divided into two regions

of near-edge and extended fine

structures.

relation between the wavelength of an electronλeand its momentuampe,thatis

λe=

h

pe

, (12.1.3)

wherehis the Planck’s constant. Using non-relativistic consideration, we can write
the momentum of the electron as

pe = meve

=

√

2 meEe, (12.1.4)

wheremeis the mass of the electron,veis its velocity, andEeis its kinetic energy
given byEe=mev^2 e/2. Substitutingpe=

√

2 meEein the above equation gives

λe=

h

√

2 meEe

. (12.1.5)

The kinetic energyEeof a photoelectron is relation to the energy of the incident
photonEγthrough
Ee=Eγ−Eb, (12.1.6)

whereEbis the binding energy o f the atom. Hence the wavelength of a photoelectron
can be evaluated from

λe=

h

√

2 me(Eγ−Eb)

. (12.1.7)

Now, the wavenumber of a particle having wavelengthλis given byk=2π/λ.The
above equation can then also be written as

2 π

k

=

h

√

2 me(Eγ−Eb)

⇒k =

[

2 me(Eγ−Eb)


^2

] 1 / 2

, (12.1.8)

where
≡=h/ 2 π. Using this expression the attenuation coefficient of the material
for x-rays can be scaled tok.Atypicalplotofμ(k) with respect tokis shown in
Fig.12.1.8. Note that the scaling ofμwith respect tokdoes not affect its shape.