9: Waves and Particles

Example number 9.1, Page number 179

In [2]:
#import modules
import math
from __future__ import division

#Variable declaration
V=20000;     #applied voltage(V)

#Calculation
lamda=12.25/(math.sqrt(V));        #de broglie wavelength(angstrom)

#Result
print "de broglie wavelength is",round(lamda,3),"angstrom"

de broglie wavelength is 0.087 angstrom

Example number 9.2, Page number 179

In [15]:
#import modules
import math
from __future__ import division

#Variable declaration
V=5000;           #applied voltage(V)
e=1.602*10**-19;     #the charge on electron(C)
m=9.12*10**-31;      #mass of electron(kg)
d=2.04*10**-10;      #distance(m)
n=1;

#Calculation
p=math.sqrt(2*m*e*V);       #momentum(kg m/s)
lamda=12.25/math.sqrt(V);       #de broglie wavelength(angstrom)
v=1/(lamda*10**-10);            #wave number
theta=math.asin((n*lamda*10**-10)/(2*d));    #Bragg angle(radian)
theta=theta*180/math.pi;                     #Bragg angle(degrees)

#Result
print "momentum is",round(p/1e-23,2),"*10^-23 kg m/s"
print "de broglie wavelength is",round(lamda,3),"angstrom"
print "the wave number is",round(v/10**10,2),"*10^10"
print "the Bragg angle is",round(theta,2),"degrees"
print "answers given in the book varies due to rounding off errors"

momentum is 3.82 *10^-23 kg m/s
de broglie wavelength is 0.173 angstrom
the wave number is 5.77 *10^10
the Bragg angle is 2.43 degrees
answers given in the book varies due to rounding off errors

Example number 9.3, Page number 179

In [18]:
#import modules
import math
from __future__ import division

#Variable declaration
V=54;           #applied voltage(V)
e=1.602*10**-19;       #the charge on electron(C)
m=9.12*10**-31;        #mass of electron(kg)
h=6.625*10**-34;       #Plank's constant

#Calculation
v=math.sqrt(2*e*V/m);      #velocity of electron(m/s)
lamda=12.25/math.sqrt(V);       #de broglie wavelength(angstrom)
u=h/(2*m*lamda*10**-10);        #phase velocity(m/s)

#Result
print "velocity of electron is",round(v/1e+6,2),"*10^6 m/s"
print "de broglie wavelength is",round(lamda,2),"angstrom"
print "phase velocity is",round(u/1e+6,2),"*10^6 m/s"

velocity of electron is 4.36 *10^6 m/s
de broglie wavelength is 1.67 angstrom
phase velocity is 2.18 *10^6 m/s

Example number 9.4, Page number 180

In [21]:
#import modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;        #the charge on electron(C)
m=9.12*10**-31;       #mass of electron(kg)
c=3*10**8;           #speed of light(m/s)
h=6.625*10**-34;     #Plank's constant

#Calculation
E=m*c**2;         #rest energy(J)
mp=1836*m;        #mass of proton(kg)
#(0.5*m*v^2)=E
mv=math.sqrt(E*2*mp);     #momentum(kg m/s)
lamda=h/mv;            #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**10,4),"Angstrom"

de broglie wavelength is 0.0004 Angstrom

Example number 9.5, Page number 180

In [23]:
#import modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;        #the charge on electron(C)
m=1.676*10**-27;      #mass of neutron(kg)
c=3*10**8;            #speed of light(m/s)
h=6.625*10**-34;      #Plank's constant

#Calculation
E=1;          #in eV
E=1*e;        #in V
mv=math.sqrt(2*E*m);         #momentum(kg m/s)
lamda=h/mv;           #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**10,3),"Angstrom"

de broglie wavelength is 0.286 Angstrom

Example number 9.6, Page number 183

In [29]:
#import modules
import math
from __future__ import division

#Variable declaration
lamda=0.09;          #wavelength(Angstrom)
D=54;            #scattering angle(degree)
h=6.625*10**-34;      #Plank's constant
c=3*10**8;            #speed of light(m/s)
e=1.6*10**-19;        #the charge on electron(C)

#Calculation
dlamda=0.0243*(1-math.cos(D));      
lamda1=lamda+dlamda;             #Wavelength of scattered X-rays(Angstrom)
Ei=h*c/(lamda*10**-10);           #Energy of incident photon(J)
Es=h*c/(lamda1*10**-10);          #Energy of scattered photon(J)

#Result
print "wavelength of scattered X-rays is",round(lamda1,1),"Angstrom"
print "Energy of incident photon is",round(Ei/(e*10**6),3),"MeV"
print "Energy of scattered photon is",round(Es/(e*10**6),4),"MeV"
print "answer for energy of scattered photon given in the book varies due to rounding off errors"

wavelength of scattered X-rays is 0.1 Angstrom
Energy of incident photon is 0.138 MeV
Energy of scattered photon is 0.0924 MeV
answer for energy of scattered photon given in the book varies due to rounding off errors

Example number 9.7, Page number 191

In [32]:
#import modules
import math
from __future__ import division

#Variable declaration
h=6.625*10**-34;      #Plank's constant
m=9.12*10**-31;       #mass of electron(kg)

#Calculation
#for 1st quantum state
nx=1;
ny=1;
nz=1;
L=1;
E1=h**2*(nx**2+ny**2+nz**2)/(8*m*L**2);       #energy in first quantum state(J)
#for 2nd quantum state (nx^2+ny^2+nz^2)=6
L=1;
E=h**2*6/(8*m*L**2);                   #energy in second quantum state(J)

#Result
print "energy in first quantum state is",round(E1/1e-37,3),"*10^-37 J"
print "energy in second quantum state is",round(E/1e-37,2),"*10^-37 J"

energy in first quantum state is 1.805 *10^-37 J
energy in second quantum state is 3.61 *10^-37 J

Example number 9.8, Page number 194

In [35]:
#import modules
import math
from __future__ import division

#Variable declaration
h=6.625*10**-34;       #Plank's constant
m=9.12*10**-31;        #mass of electron(kg)
L=2.5*10**-10;         #width of square(m)
e=1.6*10**-19;         #the charge on electron(C)
n1=1;
n2=2;
n3=3;

#Calculation
E1=n1**2*h**2/(8*m*L**2*e);          #1st lowest quantum energy(eV)
E2=n2**2*E1;             #2nd lowest quantum energy(eV)
E3=n3**2*E1;             #3rd lowest quantum energy(eV) 
 
#Result
print "the lowest 3 quantum energies are",int(E1),"eV,",int(E2),"eV and",int(E3),"eV"

the lowest 3 quantum energies are 6 eV, 24 eV and 54 eV