Chapter 15 X-Ray and diffraction of X-Ray

Example 15.1 Page no 55

In [5]:
#Given
V=100000.0
a=12400

#Calculation
w=a/V

#Result
print"Cut off wavelength is",w,"A"

Cut off wavelength is 0.124 A

Example 15.2 Page no 56

In [8]:
#Given
V=25000.0

#Calculation
w=a/V

#Result
print"Minimum wavelength is",w,"A"

Minimum wavelength is 0.496 A

Example 15.3 Page no 56

In [15]:
#Given
e=1.6*10**-19                         #C
V=10*10**3
m=9.1*10**-31                         #Kg

#Calculation
import math
v=math.sqrt((2*e*V)/m)

#Result
print"Velocity of electron is",round(v*10**-7,1),"*10**7 m/s"

Velocity of electron is 5.9 *10**7 m/s

Example 15.4 Page no 56

In [22]:
#Given
h=6.62*10**-34                         #j-s
e=1.6*10**-19                            #C
c=3*10**8
w=10**-10

#Calculation
E=((h*c)/w)/e

#Result
print"Energy of each electron is",round(E*10**-3,2),"Kev"

Energy of each electron is 12.41 Kev

Example 15.5 Page no 56

In [27]:
#Given
w=10**-10

#Calculation
V=a/w

#Result
print"Minimum applied potential is",V*10**-3,"KV"

Minimum applied potential is 1.24e+11 KV

Example 15.6 Page no 57

In [32]:
#Given
V=40*10**3                     #V
e=1.6*10**-19                   #C
w=0.310*10**-10
c=3.0*10**8

#Calculation
h=(V*e*w)/c

#Result
print"Planck's constant is",round(h*10**34,2)*10**-34,"Joule-sec"

Planck's constant is 6.61e-34 Joule-sec

Example 15.7 Page no 57

In [36]:
#Given
w=1.93
a=25
b=49.0

#Calculation
W=(a/b)**2*w

#Result
print"Ka lines for tin and barium is",round(W,1),"A"

Ka lines for tin and barium is 0.5 A

Example 15.8 Page no 57

In [41]:
#Given
R=1.1*10**7                        #/m
Z=92

#Calculation
W=4/(3*R*(Z-1)**2)

#Result
print"Wavelength is",round(W*10**10,3),"A"

Wavelength is 0.146 A

Example 15.9 Page no 58

In [50]:
#Given
I0=23.0

#Calculation
import math
x=-(10/I0)*math.log(10)*math.log10(0.5)

#Result
print"Thickness is",round(x,2),"cm"

Thickness is 0.3 cm

Example 15.10 Page no 58

In [58]:
#Given
x=1.05*10**-3                   #m
a=8930
u=2466.7                        #m

#Calculation
p=u/a

#Result
print"The mass absorption coefficient of copper is",round(p,3),"m**3/kg"

The mass absorption coefficient of copper is 0.276 m**3/kg

Example 15.11 Page no 58

In [68]:
#Given
d=2.820                          #A
q=2
a=0.1491

#Calculation
import math
l=d*a*q
l1=math.asin((q*l)/(q*d))*180/3.14

#Result
print"The wavelength of the x-ray is",round(l,3),"A"
print"The angle is",round(l1,0),"degree"

The wavelength of the x-ray is 0.841 A
The angle is 17.0 degree

Example 15.12 Page no 59

In [106]:
#Given
d=3.84*10**-8
n=2
a=10*0.05
h=6.6*10**-34
e=10**-10
m=1.67*10**-27
A=30

#Calculation
import math
l=n*d*math.sin(A*3.14/180.0)
v=(h/(m*l*10))

#Result
print"The wave length of the neutron beam is",round(l*10**8,2),"10**-8"
print"Speed is", round(v,2),"*10**3 m/sec"

The wave length of the neutron beam is 3.84 10**-8
Speed is 1.03 *10**3 m/sec

Example 15.13 Page no 59

In [109]:
#Given
l=1.8*10**-18

#Calculation
a=1*l

#Result
print"Interatomic spacing is",a,"m"

Interatomic spacing is 1.8e-18 m

Example 15.14 Page no 59

In [132]:
#Given
d=2.814
a=9                   #degree
n1=1
n2=2
n3=3
n4=4
n5=5

#Calculation
import math
l1=n2*d*math.sin(a*3.14/180.0)
l2=l1/2.0
l3=l1/3.0
l4=l1/4.0
l5=l1/5.0

#Result
print"Wavelength is",round(l1,4),"A\n",round(l2,4),"A\n",round(l3,4),"A\n",round(l4,4),"A\n",round(l5,4),"A"

Wavelength is 0.88 A
0.44 A
0.2933 A
0.22 A
0.176 A

Example 15.15 Page no 59

In [143]:
#Given
w=0.71                    #A                       
a=2.814

#Calculation
import math
A=math.asin(w/a)*180/3.14

#Result
print"The glancing angle on the cube face is",round(A,0)

The glancing angle on the cube face is 15.0

Example 15.16 Page no 60

In [151]:
#Given
w=2*10**-11
q=45
l=3

#Calculation
import math
r=1*w*math.sqrt(l)/(2*math.sin(q*3.14/180.0))

#Result
print"The interatomic spacing of the crystal is",round(r*10**11,2),"10**-11","m"

The interatomic spacing of the crystal is 2.45 10**-11 m

Example 15.17 Page no 60

In [173]:
#Given
a=5        
b=12       
c=18       
l=0.586    #A

#Calculation
import math
d=l/(2*math.sin(a*3.14/180.0))
d1=l/(math.sin(b*3.14/180.0))
d2=1/(2*math.sin(c*3.14/180.0))

#Result
print"The spacing from first maximum is",round(d,3),"A"
print"The spacing from second maximum is",round(d1,3),"A"
print"The spacing from third maximum is",round(d2,3),"A"

The spacing from first maximum is 3.363 A
The spacing from second maximum is 2.82 A
The spacing from third maximum is 1.619 A

Example 15.18 Page no 60

In [180]:
#Given
w=1.549
d=4.255
n=1
n1=2

#Calculation
import math
a=n*w/(2*d)
A=math.asin(a)*180/3.14
a1=n1*w/(2*d)
A1=math.asin(a1)*180/3.14

#Result
print"Glacing angles are",round(A,2),"degree and",round(A1,2),"Degree"

Glacing angles are 10.49 degree and 21.36 Degree

Example 15.19 Page no 61

In [193]:
#Given
a=28                    #Degree
w=0.32*10**-9
n=1

#Calculation
import math
d=n*w/(2.0*math.sin(a*3.14/180.0))

#Result
print"Distance between atomic planes is",round(d*10**9,2),"nm"

Distance between atomic planes is 0.34 nm