8: X-Rays

Example number 8.1, Page number 210

In [3]:
#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 [6]:
#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 [21]:
#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
phi = phi*math.pi/180;         #scattering angle(radian)
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)
lamdadash = math.ceil(lamdadash*10)/10;   #rounding off to 1 decimal
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 [5]:
#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
phi = phi*math.pi/180;         #scattering angle(radian)
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 [14]:
#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
phi = phi*math.pi/180;         #scattering angle(radian)
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