# 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)

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