# 8: X-Rays¶

## Example number 8.1, Page number 210¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
theta = 15;        #angle of reflection(degrees)
d = 2.5;           #atomic spacing(angstrom)
n = 1;        #first order

#Calculation
d = d*10**-10;          #atomic spacing(m)
theta = theta*math.pi/180;         #angle of reflection(radian)
lamda = 2*d*math.sin(theta)/n;          #wavelength of X-rays(m)

#Result
print "wavelength of X-rays is",round(lamda/1e-10,3),"*10**-10 m"

wavelength of X-rays is 1.294 *10**-10 m


## Example number 8.2, Page number 211¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
two_theta = 20;        #angle of reflection(degrees)
d = 2.82;           #atomic spacing(angstrom)
n = 1;        #first order

#Calculation
theta = two_theta/2;
theta = theta*math.pi/180;         #angle of reflection(radian)
lamda = 2*d*math.sin(theta)/n;          #wavelength of X-rays(angstrom)
lamda = math.ceil(lamda*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "wavelength of X-rays is",lamda,"angstrom"

wavelength of X-rays is 0.9794 angstrom


## Example number 8.3, Page number 211¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 10;       #wavelength(pm)
phi = 45;         #scattering angle(degrees)
h = 6.62*10**-34;     #planck's constant(m**2 kg/s)
m0 = 9.1*10**-31;          #mass(kg)
c = 3*10**8;        #velocity of light(m/s)
ev = 6.24*10**18;         #conversion factor from J to eV

#Calculation
a = h/(m0*c);         #value of constant(m)
a = a*10**12;         #value of constant(pm)
lamda_dash = lamda+(a*(1-math.cos(phi)));      #wavelength of X-rays(pm)
lamda_dash = math.ceil(lamda_dash*10**2)/10**2;   #rounding off to 2 decimals
lamdadash = lamda+(2*a);       #maximum wavelength of scattered x-rays(pm)
KE = h*c*((1/lamda)-(1/lamdadash))/(10**-12);          #maximum kinetic energy(J)
KE = KE*ev;           #maximum kinetic energy(eV)
KE = KE*10**-3;          #maximum kinetic energy(KeV)
KE = math.ceil(KE*10)/10;   #rounding off to 1 decimal

#Result
print "wavelength of X-rays scattered is",lamda_dash,"pm"
print "maximum wavelength of scattered x-rays is",lamdadash,"pm"
print "maximum kinetic energy is",KE,"KeV"

wavelength of X-rays scattered is 10.72 pm
maximum wavelength of scattered x-rays is 14.9 pm
maximum kinetic energy is 40.8 KeV


## Example number 8.4, Page number 212¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
h = 6.62*10**-34;     #planck's constant(m**2 kg/s)
m0 = 9.1*10**-31;          #mass(kg)
c = 3*10**8;        #velocity of light(m/s)
phi = 180;         #scattering angle(degrees)

#Calculation
a = h/(m0*c);         #value of constant(m)
a = a*10**10;         #value of constant(angstrom)
delta_lamda = a*(1-math.cos(phi));        #change in wavelength(angstrom)
delta_lamda = math.ceil(delta_lamda*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "change in wavelength of photon is",delta_lamda,"angstrom"
print "answer in the book varies due to rounding off errors"

change in wavelength of photon is 0.0485 angstrom
answer in the book varies due to rounding off errors


## Example number 8.5, Page number 212¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
h = 6.62*10**-34;     #planck's constant(m**2 kg/s)
m0 = 9.1*10**-31;          #mass(kg)
c = 3*10**8;        #velocity of light(m/s)
phi = 90;         #scattering angle(degrees)

#Calculation
a = h/(m0*c);         #value of constant(m)
a = a*10**10;         #value of constant(angstrom)
lamda = a*(1-math.cos(phi));        #wavelength(angstrom)
lamda = math.ceil(lamda*10**5)/10**5;   #rounding off to 5 decimals
E = h*c/(lamda*10**-10);          #energy of photon(J)

#Result
print "wavelength of the photon is",lamda,"angstrom"
print "energy of the incident photon is",round(E/1e-14,4),"*10**-14 J"
print "answer for energy of incident photon is wrong in the book"

wavelength of the photon is 0.02425 angstrom
energy of the incident photon is 8.1897 *10**-14 J
answer for energy of incident photon is wrong in the book