# 4: Matter Waves¶

## Example number 1, Page number 153¶

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.602*10**-19;            #charge(coulomb)
me=9.11*10**-31;            #mass(kg)
h=6.625*10**-34;            #planks constant(Js)
M=0.05;                     #mass(kg)
v=20;                       #velocity(m/sec)
vp=2200;                    #velocity of proton(m/sec)
mp=1.67*10**-27;            #mass of proton(kg)
E=10;                       #energy(eV)

#Calculations
lamda1=h/(M*v);     #de-Broglie wavelength in 1st case(m)
lamda2=h/(mp*vp);     #de-Broglie wavelength in 2nd case(m)
lamda3=h/math.sqrt(2*me*e*E);     #de-Broglie wavelength in 3rd case(m)

#Result
print "de-Broglie wavelength in 1st case is",lamda1,"m"
print "de-Broglie wavelength in 2nd case is",round(lamda2*10**10,1),"angstrom"
print "de-Broglie wavelength in 3rd case is",round(lamda3*10**10,1),"angstrom"

de-Broglie wavelength in 1st case is 6.625e-34 m
de-Broglie wavelength in 2nd case is 1.8 angstrom
de-Broglie wavelength in 3rd case is 3.9 angstrom


## Example number 2, Page number 154¶

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

#Variable declaration
h=6.63*10**-34;            #planks constant(Js)
vp=10**4;                  #velocity of proton(m/sec)
mp=1.673*10**-27;          #mass of proton(kg)
V1=100;                    #potential difference in 1st case(V)
V2=10000;                  #potential difference in 2nd case(V)
V3=6400;                  #potential difference in 3rd case(V)

#Calculations
lamda1=12.25/math.sqrt(V1);     #de-Broglie wavelength in 1st case(angstrom)
lamda2=12.25/math.sqrt(V2);     #de-Broglie wavelength in 2nd case(angstrom)
lamda3=12.25/math.sqrt(V3);     #de-Broglie wavelength in 3rd case(angstrom)
lamda4=12.25/math.sqrt(V2);     #de-Broglie wavelength in 4th case(angstrom)
lamda5=h*10**10/(mp*vp);        #de-Broglie wavelength in 5th case(angstrom)

#Result
print "de-Broglie wavelength in 1st case is",lamda1,"angstrom"
print "de-Broglie wavelength in 2nd case is",lamda2,"angstrom"
print "de-Broglie wavelength in 3rd case is",round(lamda3,5),"angstrom"
print "answer given in the book is wrong"
print "de-Broglie wavelength in 4th case is",lamda4,"angstrom"
print "de-Broglie wavelength in 5th case is",round(lamda5,4),"angstrom"

de-Broglie wavelength in 1st case is 1.225 angstrom
de-Broglie wavelength in 2nd case is 0.1225 angstrom
de-Broglie wavelength in 3rd case is 0.15313 angstrom
answer given in the book is wrong
de-Broglie wavelength in 4th case is 0.1225 angstrom
de-Broglie wavelength in 5th case is 0.3963 angstrom


## Example number 3, Page number 154¶

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

#Variable declaration
c=3*10**8;                  #velocity of light(m/sec)
mp=1.67*10**-27;            #mass of proton(kg)
h=6.62*10**-34;             #planks constant(Js)

#Calculations
v=c/20;             #velocity of proton(m/sec)
lamda=h/(mp*v);     #de-Broglie wavelength of proton(m)

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

de-Broglie wavelength of proton is 2.64 *10**-14 m


## Example number 4, Page number 155¶

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1.674*10**-27;           #mass of proton(kg)
h=6.6*10**-34;             #planks constant(Js)
lamda=10**-10;             #wavelength(m)
e=1.6*10**-19;             #charge(coulomb)

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

#Result
print "energy of neutron is",round(E*10**2,2),"*10**-2 eV"

energy of neutron is 8.13 *10**-2 eV


## Example number 5, Page number 155¶

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;           #mass of proton(kg)
h=6.62*10**-34;             #planks constant(Js)
lamda=3*10**-12;             #wavelength(m)
e=1.6*10**-19;             #charge(coulomb)

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

#Result
print "energy of neutron is",round(E,1),"eV"
print "answer given in the book is wrong"

energy of neutron is 167217.6 eV
answer given in the book is wrong


## Example number 6, Page number 155¶

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;           #mass of proton(kg)
h=6.6*10**-34;           #planks constant(Js)
lamda=0.4*10**-10;       #wavelength(m)
e=1.6*10**-19;           #charge(coulomb)

#Calculations
V=h**2/(2*m*e*lamda**2);    #voltage(V)

#Result
print "voltage is",round(V,1),"V"
print "answer given in the book is wrong"

voltage is 934.9 V
answer given in the book is wrong


## Example number 7, Page number 156¶

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1.67*10**-27;          #mass of proton(kg)
h=6.63*10**-34;          #planks constant(Js)
lamda=10**-10;           #wavelength(m)
e=1.6*10**-19;           #charge(coulomb)

#Calculations
v=h/(m*lamda);           #velocity(m/sec)
E=m*v**2/(2*e);          #kinetic energy of particle(eV)

#Result
print "velocity is",round(v/10**3,2),"*10**3 m/sec"
print "kinetic energy of particle is",round(E,5),"eV"
print "answer in the book varies due to rounding off errors"

velocity is 3.97 *10**3 m/sec
kinetic energy of particle is 0.08225 eV
answer in the book varies due to rounding off errors


## Example number 8, Page number 156¶

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

#Variable declaration
c=3*10**8;              #velocity of light(m/sec)
E=1000;                 #energy(eV)
m=9.1*10**-31;          #mass of proton(kg)
h=6.6*10**-34;          #planks constant(Js)
e=1.6*10**-19;          #charge(coulomb)

#Calculations
lamdap=h*c/(E*e);            #wavelength of photon(m)
lamdae=h/math.sqrt(2*m*e*E);    #wavelength of electron(m)

#Result
print "wavelength of photon is",round(lamdap*10**10,1),"angstrom"
print "wavelength of electron is",round(lamdae*10**10,2),"angstrom"

wavelength of photon is 12.4 angstrom
wavelength of electron is 0.39 angstrom


## Example number 9, Page number 157¶

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;              #velocity of light(m/sec)
m=9.1*10**-31;          #mass of proton(kg)
h=6.6*10**-34;          #planks constant(Js)
lamda=0.82*10**-10;     #wavelength(m)

#Calculations
E=h*c/lamda;            #energy(J)
lamda=h/math.sqrt(2*m*E);    #wavelength of photo-electron(m)

#Result
print "energy is",round(E*10**15,1),"*10**-15 J"
print "wavelength of photo-electron is",round(lamda*10**10,1),"angstrom"

energy is 2.4 *10**-15 J
wavelength of photo-electron is 0.1 angstrom


## Example number 10, Page number 157¶

In [47]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;              #velocity of light(m/sec)
m=9.1*10**-31;          #mass of proton(kg)
h=6.6*10**-34;          #planks constant(Js)

#Calculations
lamda=h/(m*c);          #wavelength of quantum(m)

#Result
print "wavelength of quantum is",round(lamda*10**10,4),"angstrom"
print "answer in the book varies due to rounding off errors"

wavelength of quantum is 0.0242 angstrom
answer in the book varies due to rounding off errors


## Example number 11, Page number 158¶

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=10**14;               #kinetic energy(eV)
e=1.6*10**-19;          #charge(coulomb)
m=1.675*10**-27;        #mass of proton(kg)
h=6.625*10**-34;        #planks constant(Js)

#Calculations
v=math.sqrt(2*e*E/m);   #velocity(m/sec)
lamda=h/(m*v);          #de-broglie wavelength(m)

#Result
print "de-broglie wavelength is",round(lamda*10**18,2),"*10**-18 m"

de-broglie wavelength is 2.86 *10**-18 m


## Example number 12, Page number 158¶

In [56]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=12.8*10**6;               #kinetic energy(eV)
e=1.6*10**-19;          #charge(coulomb)
m=1.675*10**-27;        #mass of proton(kg)
h=6.625*10**-34;        #planks constant(Js)

#Calculations
v=math.sqrt(2*e*E/m);   #velocity(m/sec)
lamda=h/(m*v);          #de-broglie wavelength(m)

#Result
print "de-broglie wavelength is",round(lamda*10**15,3),"*10**-15 m"
print "answer given in the book is wrong"

de-broglie wavelength is 7.998 *10**-15 m
answer given in the book is wrong


## Example number 13, Page number 158¶

In [64]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=12.8*10**6;           #kinetic energy(eV)
c=3*10**8;              #velocity of light(m/sec)
m=9.1*10**-31;          #mass of electron(kg)
mp=1836*m;              #mass of proton(kg)
h=6.625*10**-34;        #planks constant(Js)
e=1.6*10**-19;          #charge(coulomb)

#Calculations
E=m*c**2;               #energy(J)
v=math.sqrt(2*E/mp);    #velocity(m/sec)
lamda=h/(mp*v);          #de-broglie wavelength(m)

#Result
print "de-broglie wavelength is",round(lamda*10**10,4),"angstrom"
print "answer given in the book is wrong"

de-broglie wavelength is 0.0004 angstrom
answer given in the book is wrong


## Example number 14, Page number 159¶

In [70]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;                #temperature(K)
m=1.67*10**-27;       #mass of electron(kg)
h=6.60*10**-34;       #planks constant(Js)
k=8.6*10**-5;         #boltzmann constant(eV deg-1)
e=1.6*10**-19;        #charge(coulomb)

#Calculations
lamda=h/math.sqrt(2*m*e*k*T);     #wavelength(m)

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

wavelength is 1.777 angstrom


## Example number 16, Page number 160¶

In [77]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=0.512*10**6;          #kinetic energy(eV)
e=1.6*10**-19;          #charge(coulomb)
m=1.673*10**-27;        #mass of proton(kg)
h=6.63*10**-34;         #planks constant(Js)

#Calculations
v=2*e*E/m;   #velocity(m/sec)
lamda=h*10**10/(m*v);          #de-broglie wavelength(angstrom)

#Result
print "de-broglie wavelength is",round(lamda*10**11,3),"*10**11 angstrom"
print "answer given in the book is wrong"

de-broglie wavelength is 4.047 *10**11 angstrom
answer given in the book is wrong


## Example number 17, Page number 160¶

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

#Variable declaration
E=0.512*10**6;          #rest mass energy(eV)
e=1.6*10**-19;          #charge(coulomb)
KE=1.512*10**6;         #kinetic energy(eV)
c=3*10**8;              #velocity of light(m/sec)
m0=9.1*10**-31;         #mass of proton(kg)
h=6.63*10**-34;         #planks constant(Js)

#Calculations
E1=(E+KE)*e;                #energy(J)
m=E1/c**2;                   #mass(kg)
v=math.sqrt(c**2*(1-(m0/m)**2));      #velocity(m/sec)
lamda=h*10**10/(m*v);          #de-broglie wavelength(angstrom)

#Result
print "de-broglie wavelength is",round(lamda,6),"angstrom"

de-broglie wavelength is 0.006348 angstrom


## Example number 18, Page number 161¶

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

#Variable declaration
k=1.38*10**-23;        #boltzmann constant
T=300;                 #temperature(K)
m0=1.67*10**-27;       #mass of proton(kg)
h=6.6*10**-34;         #planks constant(Js)

#Calculations
lamda=h/math.sqrt(3*m0*k*T);          #de-broglie wavelength(metre)

#Result
print "de-broglie wavelength is",round(lamda*10**10,2),"*10**-10 metre"
print "answer in the book varies due to rounding off errors"

de-broglie wavelength is 1.45 *10**-10 metre
answer in the book varies due to rounding off errors


## Example number 19, Page number 162¶

In [11]:
#importing modules
import math
from __future__ import division

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

#Calculations
E=k*T;                 #energy(J)
p=math.sqrt(2*mn*E);
d=h*10**10/p;                 #interplanar spacing(angstrom)

#Result
print "interplanar spacing is",round(d,2),"angstrom"

interplanar spacing is 1.78 angstrom


## Example number 20, Page number 162¶

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

#Variable declaration
m=9*10**-31;       #mass of proton(kg)
e=1.6*10**-19;     #charge(coulomb)
V=344;             #voltage(V)
h=6.62*10**-34;    #planks constant(Js)

interplanar spacing is 0.4 angstrom