# Chapter 3: Characterisation of material¶

## Example 3.1, page no-89¶

In [1]:
# wavelength and frequency of X-rays

import math
#Variable Declaration
h=6.626*10**-34                    # Planck's constant
e=1.6*10**-19                      # charge of an electron
c=3.0*10**8                        # speed of light
v=10000.0                          # Applied potential difference

#Calculation
lam_min=(h*c)/(e*v)
V=c/lam_min

#Result
print('\n(i)\nThe wavelength of X-rays emitted Lamda_min = %.2f A°\n(ii)\nThe frequency of X-ray beam emitted is %.1f*10^18 Hz'%(lam_min*10**10,V*10**-18))

(i)
The wavelength of X-rays emitted Lamda_min = 1.24 A°
(ii)
The frequency of X-ray beam emitted is 2.4*10^18 Hz


## Example 3.2, page no-89¶

In [4]:
# wavelength and velocity of electrons

import math
#Variable Declaration

v=10000.0                     # Applied potential difference
i=2*10**-3                    # Current
e=1.6*10**-19                 # charge of an electron
t=1.0                         # time in second
m=9.1*10**-31                 # mass of an electrons

#(i)

#Calculation
n=i*t/e

#Result
print('The no of electrons striking the target per second =%.2f *10^16'%(n*10**-16))

#(ii)

#Calculation
v1=math.sqrt(2*e*v/m)

#(iii)

#Calculation
lam=12400.0/v

#Result
print('\n(ii)\nThe velocity of electron =%.2f*10^7 m/s\n(iii)\nWavelength of x-rays=%.2f A°'%(v1*10**-7,lam))

The no of electrons striking the target per second =1.25 *10^16

(ii)
The velocity of electron =5.93*10^7 m/s
(iii)
Wavelength of x-rays=1.24 A°


## Example 3.3, page no-90¶

In [5]:
# wavelength and angle for 2nd order bragg reflection

import math
#variable Declaration
d=5.6534*10**-10             # interplanar spacing
theta=13.6666                # glancing angle
n=1.0                        # order of diffraction

#(i)
#Calculation
lam=2*d*math.sin(theta*math.pi/180)/n

#Result
print('\n(i)\nWavelength of the X-rays, Lambda =%.3f*10^-10 m'%(lam*10**10))

#(ii)
#calculation
n=2.0
theta=math.asin(n*lam/(2*d))
theta=theta*180/math.pi

#Result
print('\n(ii)\n2nd order Bragg reflection at angle Theta2 = %f°'%theta)

(i)
Lambda =2.671*10^-10 m

(ii)
2nd order Bragg reflection at angle Theta2 = 28.199528°


## Example 3.4, page no-91¶

In [9]:
# Grating spacing and glancing angle

import math
#Variable Declaration
v=24800.0                    # Applied potential difference
n=1.0                        # order of diffraction
lam=1.54*10**-10             # wavelength of the X-ray beam
ga=15.8                      # glancing angle

#(i)

#calculation
d=n*lam/(2*math.sin(ga*math.pi/180))

#Result
print('\n(i)\nGrating spacing for NaCl crystal =%.3f *10^-10 m'%(d*10**10))

#(ii)

#calculation
lam_min=12400.0/v
lam_min=lam_min*10**-10
theta=math.asin(n*lam_min/(2*d))
theta=theta*180/math.pi

#Result
print('\n(ii)\nGlancing angle for minimum wavelength = %.3f degrees'%theta)
# Glancing angle in the book is in the degree second format

(i)
Grating spacing for NaCl crystal =2.828 *10^-10 m

(ii)
Glancing angle for minimum wavelength = 5.072 degrees


## Example 3.5, page no-92¶

In [10]:
# wavelength of radiation

import math
#variable Declaration
lam=0.7078 *10**-10                   # wavelength of Ka line from molybdenum
wt=42.0                               # Atomic number of molybdenum
wt1=48.0                              # Atomic number of cadmium

#calculation
lam1=(lam*(wt-1)**2)/(wt1-1)**2

#Result

Wavelength of cadmium radiation is 0.5386 A°


## Example 3.6, page no-92¶

In [12]:
# Energy of thermal neutron

import math
#Variable Declaration
lam=10.0**-10                           # Wavelength of neutron
h=6.626*10**-34                         # Planck's constant
m=1.675*10**-27                         # mass of an electron
e1=1.602*10**-19                        # charge of an electron

#calculation
e=(h**2)/(2*m*lam**2)
e=e/e1

#Result
print('\nThe energy of thermal neutron with wavelength 1 A° is %.2f eV'%e)

The energy of thermal neutron with wavelength 1A° is 0.08 eV


## Example 3.8, page no-94¶

In [1]:
# effect of temperature on wavelength

import math
#Variable Declaration
lam=0.1                                # Wavelength of neutron in nm

#calculation
T=(2.516**2)/(lam)**2

#Result
print('Temperature of thermal neutron corresponding to 1 A° is %.0f K'%T)

Temperature of thermal neutron corresponding to 1 A° is 633 K