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)
theta=60*math.pi/180;     #angle(radian)

#Calculations
d=h*10**10/(2*math.sin(theta)*math.sqrt(2*m*e*V));     #spacing of crystal(angstrom)

#Result
print "interplanar spacing is",round(d,1),"angstrom"
print "answer given in the book is wrong"

interplanar spacing is 0.4 angstrom
answer given in the book is wrong