4: Matter Waves

Example number 1, Page number 158

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

#Variable declaration  
m=1.67*10**-27;            #mass of proton(kg)
h=6.625*10**-34;           #planks constant(Js)
v=3967;                    #velocity of proton(m/s)

#Calculations
lamda=h/(m*v);             #de-Broglie wavelength of proton(m)

#Result
print "de-Broglie wavelength of proton is",int(lamda*10**10),"angstrom"

de-Broglie wavelength of proton is 1 angstrom

Example number 2, Page number 158

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration  
m=9.11*10**-31;            #mass of electron(kg)
h=6.625*10**-34;           #planks constant(Js)
lamda=5*10**-10;           #de-Broglie wavelength(m)
e=1.6*10**-19;             #charge(coulomb)

#Calculations
E=h**2/(2*m*lamda**2*e);     #kinetic energy of electron(eV)

#Result
print "kinetic energy of electron is",int(E),"eV"

kinetic energy of electron is 6 eV

Example number 3, Page number 158

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration  
c=3*10**8;                  #velocity of light(m/sec)
m=1.67*10**-27;            #mass of proton(kg)
h=6.625*10**-34;             #planks constant(Js)

#Calculations
v=c/30;             #velocity of proton(m/sec)
lamda=h/(m*v);     #de-Broglie wavelength of proton(m)

#Result
print "de-Broglie wavelength of proton is",round(lamda*10**14,2),"*10**-6 angstrom"

de-Broglie wavelength of proton is 3.97 *10**-6 angstrom

Example number 4, Page number 159

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration  
V=150;          #potential difference(V)

#Calculations
lamda=12.26/math.sqrt(V);     #de-Broglie wavelength of electron(angstrom)

#Result
print "de-Broglie wavelength of electron is",int(lamda),"angstrom"

de-Broglie wavelength of electron is 1 angstrom

Example number 5, Page number 159

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration 
V=100;                 #voltage(eV)  
m=9.1*10**-31;         #mass of proton(kg)
h=6.625*10**-34;       #planks constant(Js)
e=1.6*10**-19;         #charge(coulomb)

#Calculations
lamda=h*10**10/math.sqrt(2*m*e*V);    #de-Broglie wavelength(angstrom)

#Result
print "de-Broglie wavelength is",round(lamda,2),"angstrom"

de-Broglie wavelength is 1.23 angstrom

Example number 6, Page number 159

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

#Variable declaration  
m=1.67*10**-27;            #mass of proton(kg)
h=6.625*10**-34;           #planks constant(Js)
v=4000;                    #velocity of proton(m/s)

#Calculations
lamda=h*10**10/(m*v);             #de-Broglie wavelength of neutron(angstrom)

#Result
print "de-Broglie wavelength of neutron is",round(lamda,2),"angstrom"

de-Broglie wavelength of neutron is 0.99 angstrom

Example number 7, Page number 160

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

#Variable declaration  
mp=1.67*10**-27;            #mass of proton(kg)
me=9.11*10**-31;            #mass of electron(kg)

#Calculations
r=mp/me;                    #ratio of kinetic energies of electron and proton

#Result
print "ratio of kinetic energies of electron and proton is",int(r)

ratio of kinetic energies of electron and proton is 1833

Example number 8, Page number 160

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration 
m=9.1*10**-31;         #mass of proton(kg)
e=1.6*10**-19;         #charge(coulomb)
c=3*10**8;             #velocity of light(m/sec)
E=1000;                #energy(eV)

#Calculations
r=math.sqrt(2*m/(e*E))*c;    #ratio of wavelengths

#Result
print "ratio of wavelengths is",int(round(r))

ratio of wavelengths is 32

Example number 9, Page number 160

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration 
m=9.1*10**-31;         #mass of electron(kg)
c=3*10**8;             #velocity of light(m/sec)
h=6.6*10**-34;         #planks constant(Js)
lamda=1.54*10**-10;    #wavelength of X-ray(m)
wf=1*10**-15;          #work function(J)

#Calculations
E=h*c/lamda;           #energy of X-ray(J)
Ee=E-wf;               #energy of electron emitted(J)
lamda=h/math.sqrt(2*m*Ee);     #wavelength of electron(m)

#Result
print "wavelength of electron is",round(lamda*10**10,3),"angstrom"

wavelength of electron is 0.289 angstrom

Example number 10, Page number 161

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

#Variable declaration 
m=1.67*10**-27;         #mass of proton(kg)
h=6.6*10**-34;          #planks constant(Js)
T=400;                  #temperature(K)
k=1.38*10**-23;         #boltzmann constant

#Calculations
lamda=h*10**10/math.sqrt(2*m*k*T);     #de broglie wavelength of proton(angstrom)

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

de broglie wavelength of proton is 1.537 angstrom

Example number 11, Page number 162

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration 
m=1.673*10**-27;        #mass of proton(kg)
m0=9.1*10**-31;         #mass of electron(kg)
c=3*10**8;              #velocity of light(m/sec)
h=6.63*10**-34;         #planks constant(Js)
ke=1000;                #kinetic energy

#Calculations
re=m0*c**2;             #rest energy of electron(J)
Ep=ke*re;               #energy of proton(J)
v=math.sqrt(2*Ep/m);     #velocity of proton(m/s)
lamda=h*10**10/(m*v);   #debroglie wavelength of proton(angstrom)

#Result
print "rest energy of electron is",re,"J"
print "energy of proton is",Ep,"J"
print "velocity of proton is",v,"m/s"
print "wavelength of electron is",round(lamda*10**5,2),"*10**-5 angstrom"
print "answers given in the book are wrong"

rest energy of electron is 8.19e-14 J
energy of proton is 8.19e-11 J
velocity of proton is 312902460.506 m/s
wavelength of electron is 1.27 *10**-5 angstrom
answers given in the book are wrong

Example number 12, Page number 162

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

#Variable declaration 
m=9.1*10**-31;         #mass of electron(kg)
h=6.625*10**-34;       #planks constant(Js)
lamda=0.16*10**-10;    #debroglie wavelength of electron(m)
e=1.6*10**-19;         #charge(coulomb)

#Calculations
v=h/(lamda*m);         #velocity of electron(m/s)
KE=m*v**2/(2*e);       #kinetic energy(eV)

#Result
print "velocity of electron is",round(v*10**-7,2),"*10**7 m/s"
print "kinetic energy is",int(KE),"eV"

velocity of electron is 4.55 *10**7 m/s
kinetic energy is 5887 eV

Example number 13, Page number 163

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration 
m=1.67*10**-27;       #mass of proton(kg)
h=6.62*10**-34;       #planks constant(Js)
T=300;                 #temperature(K)
k=1.38*10**-23;        #boltzmann constant

#Calculations
d=h*10**10/math.sqrt(2*m*k*T);     #interplanar spacing of crystal(angstrom)

#Result
print "interplanar spacing of crystal is",round(d,2),"angstrom"
print "answer given in the book is wrong"

interplanar spacing of crystal is 1.78 angstrom
answer given in the book is wrong

Example number 14, Page number 164

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration 
lamda=0.5;        #wavelength(angstrom)

#Calculations
V=(12.3/lamda)**2;    #potential(volts)

#Result
print "potential is",V,"volts"

potential is 605.16 volts

Example number 15, Page number 164

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

#Variable declaration 
lamda=1*10**-10;      #wavelength(m)
h=6.63*10**-34;       #planks constant(Js)
c=3*10**8;            #velocity of light(m/sec)

#Calculations
p=h/lamda;            #momentum(J-sec/m)
E=p*c;                #energy of gama ray photon(J)

#Result
print "energy of gama ray photon is",E*10**16,"*10**-16 J"

energy of gama ray photon is 19.89 *10**-16 J

Example number 16, Page number 164

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration 
h=6.6*10**-34;       #planks constant(Js)
m=9*10**-31;         #mass of electron(kg)
r=0.53*10**-10;      #radius of orbit(m)

#Calculations
v=h/(2*math.pi*r*m);   #velocity of electron(m/sec)

#Result
print "velocity of electron is",round(v*10**-6,1),"*10**6 m/sec"

velocity of electron is 2.2 *10**6 m/sec