8: X-rays

Example number 8.1, Page number 197

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=4.255;     #atomic spacing(angstrom)
lamda=1.549;   #wavelength of K-copper line(angstrom) 
n=1;    #theta is smallest when n=1


#Calculation
theta=math.asin(lamda/(2*d));   #glancing angle(radian)
theta=theta*(180/math.pi);      #glancing angle(degrees)
#max value of sin(theta)=1 for highest order
nmax=((2*d)/lamda);   #highest bragg's order


#Result
print "smallest glancing angle is",round(theta,4),"degrees"
print "maximum order of reflection is",round(nmax,3)

smallest glancing angle is 10.4875 degrees
maximum order of reflection is 5.494

Example number 8.2, Page number 197

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=60*10**3;     #potential difference(volts)
c=3*10**8;     #velocity of light(m/sec)
e=1.6*10**-19;  #electron charge(coulomb)
lamda=0.194*10**-10;  #minimum wavelength of x-rays(m)

#Calculation
h=(lamda*e*V)/c;    #planck's constant(Jsec)

#Result
print "planck's constant is",h,"Jsec"

planck's constant is 6.208e-34 Jsec

Example number 8.3, Page number 198

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
#for 110 plane
h=1;
k=1;
l=0;
a=3;   #lattice parameter(angstrom)
n=1;
theta=12.5;    #glancing angle(degrees)

#Calculation
theta1=theta*(math.pi/180);  #glancing angle(radian)
d110=(a/math.sqrt((h**2)+(k**2)+(l**2)));   
lamda=2*d110*math.sin(theta1)/n;   #wavelength of x-ray(angstrom)
nmax=((2*d110)/lamda);    #highest order possible

#Result
print "wavelength of x-ray beam is",round(lamda,3),"angstrom"
print "highest bragg's order possible is",int(nmax)

wavelength of x-ray beam is 0.918 angstrom
highest bragg's order possible is 4

Example number 8.4, Page number 198

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=2.81*10**-10;     #interplanar spacing(m)
theta=14;   #glancing angle(degrees) 
e=1.6*10**-19;   #electron charge(c)
V=9100;    #voltage(V)
n=1;
c=3*10**8;   #velocity of light(m/sec)

#Calculation
theta=theta*(math.pi/180);  #glancing angle(radian)
lamda=2*d*math.sin(theta)/n;   #minimum wavelength
h=(lamda*e*V)/c;        #planck's constant(Jsec)

#Result
print "planck's constant is",round(h*10**34,4),"*10**-34 Jsec"

planck's constant is 6.5986 *10**-34 Jsec

Example number 8.5, Page number 198

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
thetaA=30;     #glancing angle for line A(degrees)
lamdaB=0.97;    #wavelength of line B(angstrom)
thetaB=60;     #glancing angle for line B(degrees)

#Calculation
#for line A-> 2*d*sin(thetaA)=lamdaA(n=1)
thetaA=thetaA*(math.pi/180);  #glancing angle for line A(radian)
#for line B-> 2*d*sin(thetaB)=3*lamdaB(n=3)
thetaB=thetaB*(math.pi/180);  #glancing angle for line B(radian) 
d=(3*lamdaB)/(2*math.sin(thetaB));    #interplanar spacing(angstrom)
lamdaA=2*d*math.sin(thetaA);   #wavelength of line A(angstrom)

#Result
print "wavelength of line A is",round(lamdaA,2),"angstrom"

wavelength of line A is 1.68 angstrom

Example number 8.6, Page number 199

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=3.615;    #lattice constant(angstrom)
h=1;
k=1;
l=1;
theta=21.7;   #glancing angle(degrees)

#Calculation
d111=a/math.sqrt(h**2+k**2+l**2);   #interplanar spacing(angstrom)
theta=theta*(math.pi/180);   #glancing angle(radian)
lamda=2*d111*math.sin(theta);   #wavelength of X-rays(angstrom)

#Result
print "wavelength of X-rays is",round(lamda,3),"angstrom"

wavelength of X-rays is 1.543 angstrom

Example number 8.7, Page number 199

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=50*10**3;   #voltage(V)
n=4;    #FCC crystal
m=74.6;  #molecular mass(kg)
N=6.02*10**26;    #avagadro number(per kg mol)
rho=1.99*10**3;   #density(kg/m**3) 

#Calculation
lamda=(12400/V);   #short wavelength(angstrom)
a=(((n*m)/(N*rho))**(1/3));   #lattice constant(m)
#for kcl ionic crystal
d=a/2;
sintheta=lamda*10**-10/(2*d);   #value of sintheta
theta=math.asin(sintheta);    #glancing angle(radian)
theta=theta*(180/math.pi);      #glancing angle(degrees)

#Result
print "short wavelength of spectrum from tube is",lamda,"angstrom"
print "glancing angle for that wavelength is",round(theta,4),"degrees"

short wavelength of spectrum from tube is 0.248 angstrom
glancing angle for that wavelength is 2.2589 degrees

Example number 8.8, Page number 199

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
theta1=5.4;    #glancing angle(degrees)
theta2=7.6;    #glancing angle(degrees)
theta3=9.4;    #glancing angle(degrees) 

#Calculation
#from bragg's law 2*d*sin(theta)=n*lamda, n=1
theta1=theta1*(math.pi/180);   #glancing angle(radian)
theta2=theta2*(math.pi/180);   #glancing angle(radian)
theta3=theta3*(math.pi/180);   #glancing angle(radian)
d100=lamda/2*math.sin(theta1);  #interplanar spacing
d110=lamda/2*math.sin(theta2);  #interplanar spacing
d111=lamda/2*math.sin(theta3);  #interplanar spacing

#Result
print "ratio of interplanar spacing (1/d100):(1/d110):(1/d111)=",round(math.sin(theta1),4),":",round(math.sin(theta2),4),":",round(math.sin(theta3),4)
print "as ratio (1/d100):(1/d110):(1/d111)=1:sqrt(2):sqrt(3). this relation is valid for simple cubic systems. therefore, this is a simple cubic crystal"

ratio of interplanar spacing (1/d100):(1/d110):(1/d111)= 0.0941 : 0.1323 : 0.1633
as ratio (1/d100):(1/d110):(1/d111)=1:sqrt(2):sqrt(3). this relation is valid for simple cubic systems. therefore, this is a simple cubic crystal