# Chapter 5:X-Rays and X-Ray Spectra¶

## Example no:1,Page no:535¶

In :
#Variable declaration
ch=12400.0                                                                        #product of speed of light and Plank's constant (eV*Å)
lembda1=0.024                                                                   #Compton wavelength of X-ray (Å)
lembda2=1.0                                                                       #wavelength of X-ray (Å)

#Calculation
#(i)
x1=ch/lembda1                                                                   #minimum voltage across X-ray tube (V)
#(ii)
x2=ch/(lembda2*10**3)                                                            #minimum voltage across X-ray tube (kV)
#(iii)
x3=1.02                                                                         #minimum energy of X-ray photon (M*eV)

#Result
print"\n(i) voltage =%.2e"%x1,"V\n(ii) voltage =",x2,"KV\n(iii) energy =",x3,"MeV"
print"NOTE:Wrong answer of (i) in book"

(i) voltage =5.17e+05 V
(ii) voltage = 12.4 KV
(iii) energy = 1.02 MeV
NOTE:Wrong answer of (i) in book


## Example no:2,Page no:535¶

In :
#Variable declaration
n=3/2.0
dlembda=26*10**-2                                                                #shifting in short wave limit of X-ray spectrum (Å)
ch=12400                                                                        #product of speed of light and Plank's constant (eV*Å)
e=1.6*10**-19                                                                    #charge of electron (Coulomb)

#Calculation
V=((n-1)/n)*(ch/(dlembda*10**3))                                               #initial voltage applied to the tube (KV)

#Result
print"\nInitial voltage =",round(V,1),"KV"

Initial voltage = 15.9 KV


## Example no:3,Page no:535¶

In :
#Variable declaration
R=10972900.0                                                                      #(m-1)
lembda=1.54*10**-10                                                              #wavelength of K line (m)

#calculation
import math
z=1+math.sqrt(4.0/(3.0*lembda*R))                                                        #atomic number of the target element

#Result
print"\nZ =",round(z)

Z = 29.0


## Example no:4,Page no:536¶

In :
#Variable declaration
z1=29.0                                                                           #atomic no. of Copper
z2=26.0                                                                           #atomic no. of Iron
lembda1=193.0                                                                     #wavelength of K line in Iron (pm)

#calculation
lembda=((z2-1)/(z1-1))**2*lembda1                                                #wavelength of K line in Copper (pm)

#Result
print"\nλ =",round(lembda),"pm"

λ = 154.0 pm


## Example no:5,Page no:536¶

In :
#Variable declaration
z1=13                                                                           #atomic no. of Al
z2=27                                                                           #atomic no. of Co
R=1.097*10**7                                                                    #(m-1)

#calculation
lembda1=(4*10**12)/(3*R*(z1-1)**2)                                                #wavelength of K line in Al (pm)
lembda2=(4*10**12)/(3*R*(z2-1)**2)                                                #wavelength of k line in Co (pm)

#Result
print"\n wavelength of Al =",round(lembda1),"pm\n wavelength of Co =",round(lembda2),"pm"

 wavelength of Al = 844.0 pm
wavelength of Co = 180.0 pm


## Example no:6,Page no:536¶

In :
#Variable declaration
lembda1=250.0*10**-12                                                              #wavelength of K-alpha line (m)
lembda2=179.0*10**-12                                                              #wavelength of K-alpha line (m)
R=10972900.0                                                                      #(m-1)

#calculation
import math
z1=int(1+math.sqrt(4/(3*lembda1*R)))                                                      #atomic number
z2=int(1+math.sqrt(4/(3*lembda2*R)))

#Result
print"\nThe required elements are: Z ="
for i in range(z1+1,z2):
print i

The required elements are: Z =
24
25
26


## Example no:7,Page no:536¶

In :
#Variable declaration
ch=12400.0                                                                        #product of speed of light and Plank's constant (eV*Å)
Rch=13.6                                                                        #product of speed of light, Plank's constant and R (eV)
lembda=24.0                                                                       #wavelength of L absorption edge (Å)

#calculation
El=ch/(lembda*1000)                                                             #binding energy of L electron (KeV)
Ek=((3/(4.0*10**3))*Rch*(z-1)**2)+El                                                #binding energy of K electron (KeV)
#Result
print"\nBinding energy of K-electron =",round(Ek,2),"KeV"


Binding energy of K-electron = 5.45 KeV


## Example no:8,Page no:537¶

In :
#Variable declaration
ch=12.4                                                                         #product of speed of light and Plank's constant (KeV*Å)
lembda1=0.178                                                                   #wavelength of K-alpha line (Å)
lembda2=0.210                                                                   #wavelength of K line (Å)

#calculation
Ek=ch/lembda1                                                                   #binding energy of K electron (KeV)
El=Ek-(ch/lembda2)                                                              #binding energy of K-alpha electron (KeV)
lembda=ch/El                                                                   #wavelength of L absorption edge (Å)

#Result
print"\nWavelength of L absorption edge =",round(lembda,2),"Å"

Wavelength of L absorption edge = 1.17 Å


## Example no:9,Page no:537¶

In :
#Variable declaration
ch=12.4                                                                         #product of speed of light and Plank's constant (KeV*Å)
lembdak=0.18                                                                    #wavelength of K absorption edge (Å)
lembda=0.1                                                                      #wavelength of incident photon (Å)

#calculation
Ek=ch/lembdak                                                                   #binding energy of K electron (KeV)
E=ch/lembda                                                                     #energy of incident photon (KeV)
K=E-Ek                                                                          #maximum kinetic energy of ejected electron (KeV)

#Result
print"KE =",round(K,2),"KeV"

KE = 55.11 KeV


## Example no:10,Page no:538¶

In :
#Variable declaration
ch=12.4                                                                         #product of speed of light and Plank's constant (KeV*Å)
Rch=13.6/10**3                                                                   #product of speed of light, Plank's constant and R (KeV)
lembdak=1.74                                                                    #K band absorption edge wavelength of iron (Å)
z=30                                                                            #atomic no. of zinc

#calculation
Ek=ch/lembdak                                                                   #binding energy of K electron in iron (KeV)
E=(3.0/4.0)*Rch*(z-1)**2                                                             #energy of photon of K-alpha radiation (KeV)
K=E-Ek                                                                          #kinetic energy of the photoelectrons liberated from iron (KeV)

#Result
print"KE =",round(K,3),"KeV"

KE = 1.452 KeV