6: Principles of quantum mechanics

Example number 6.1, Page number 6.8

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;     #velocity of light(m/s)
m=1.67*10**-27;     #mass of proton(kg)
h=6.626*10**-34;    #planck's constant

#Calculation
lamda=h*10/(m*c);     #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**14,3),"*10**-14 m"

de broglie wavelength is 1.323 *10**-14 m

Example number 6.2, Page number 6.8

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

#Variable declaration
V=400;    #voltage(V)

#Calculation
lamda=12.26/math.sqrt(V);      #de broglie wavelength(angstrom)

#Result
print "de broglie wavelength is",lamda,"angstrom"

de broglie wavelength is 0.613 angstrom

Example number 6.3, Page number 6.8

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

#Variable declaration
m=1.674*10**-27;     #mass of proton(kg)
h=6.626*10**-34;    #planck's constant
E=0.025*1.6*10**-19;    #energy(J)

#Calculation
lamda=h/math.sqrt(2*m*E);     #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**9,3),"nm"

de broglie wavelength is 0.181 nm

Example number 6.4, Page number 6.9

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

#Variable declaration
V=1600;    #voltage(V)

#Calculation
lamda=12.26/math.sqrt(V);      #de broglie wavelength(angstrom)

#Result
print "de broglie wavelength is",lamda,"angstrom"

de broglie wavelength is 0.3065 angstrom

Example number 6.5, Page number 6.14

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
deltax=0.2*10**-10;      #distance(m)
h=6.626*10**-34;    #planck's constant

#Calculation
deltap=h/(2*math.pi*deltax);    #uncertainity in momentum(kg m/s)

#Result
print "uncertainity in momentum is",round(deltap*10**24,2),"*10**-24 kg m/s"

uncertainity in momentum is 5.27 *10**-24 kg m/s

Example number 6.6, Page number 6.21

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

#Variable declaration
n1=n2=n3=1;
h=6.62*10**-34;    #planck's constant
m=9.1*10**-31;     #mass(kg)
L=0.1*10**-9;      #side(m) 

#Calculation
E1=h**2*(n1**2+n2**2+n3**2)/(8*m*1.6*10**-19*L**2);    #lowest energy of electron(eV)

#Result
print "lowest energy of electron is",round(E1,1),"eV"

lowest energy of electron is 112.9 eV

Example number 6.7, Page number 6.22

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=n2=n3=1;
h=6.62*10**-34;    #planck's constant
m=8.5*10**-31;     #mass(kg)
L=10**-11;      #side(m) 

#Calculation
E111=h**2*(n1**2+n2**2+n3**2)/(8*m*1.6*10**-19*L**2);    #lowest energy of electron(eV)
E112=6*h**2/(8*m*1.6*10**-19*L**2);      #value of E112(eV)
E121=E112;      #value of E121(eV)
E211=E112;      #value of E211(eV)
E122=9*h**2/(8*m*1.6*10**-19*L**2);     #value of E122(eV)
E212=E122;      #value of E212(eV)
E221=E122;      #value of E221(eV)

#Result
print "lowest energy of electron is",round(E111/10**4,3),"*10**4 eV"
print "value of E112, E121, E211 is",round(E121/10**4,4),"*10**4 eV"
print "value of E122, E212, E221 is",round(E122/10**4,3),"*10**4 eV"

lowest energy of electron is 1.208 *10**4 eV
value of E112, E121, E211 is 2.4168 *10**4 eV
value of E122, E212, E221 is 3.625 *10**4 eV

Example number 6.8, Page number 6.23

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

#Variable declaration
m=9.1*10**-31;     #mass of electron(kg)
h=6.626*10**-34;    #planck's constant
E=2000*1.6*10**-19;    #energy(J)

#Calculation
lamda=h/math.sqrt(2*m*E);     #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**9,4),"nm"

de broglie wavelength is 0.0275 nm

Example number 6.9, Page number 6.23

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

#Variable declaration
m=9.1*10**-31;     #mass of electron(kg)
h=6.626*10**-34;    #planck's constant
n=1;
L=4*10**-10;      #side(m) 

#Calculation
E1=n**2*h**2/(8*m*L**2);    #lowest energy of electron(joule)


#Result
print "lowest energy of electron is",round(E1*10**18,3),"*10**-18 joule"
print "answer varies due to rounding off errors"

lowest energy of electron is 0.377 *10**-18 joule
answer varies due to rounding off errors

Example number 6.10, Page number 6.24

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

#Variable declaration
m=9.1*10**-31;     #mass of electron(kg)
h=6.626*10**-34;    #planck's constant
n1=1;
n2=2;
n3=3;
L=1*10**-10;      #side(m) 

#Calculation
E1=n1**2*h**2/(8*m*L**2);    #lowest energy of electron(joule)
E2=n2**2*h**2/(8*m*L**2);    #energy of electron in 1st state(joule)
E3=n3**2*h**2/(8*m*L**2);    #energy of electron in 2nd state(joule)

#Result
print "lowest energy of electron is",round(E1*10**17,4),"*10**-17 joule"
print "energy of electron in 1st state is",round(E2*10**17,3),"*10**-17 joule"
print "energy of electron in 2nd state is",round(E3*10**17,3),"*10**-17 joule"

lowest energy of electron is 0.6031 *10**-17 joule
energy of electron in 1st state is 2.412 *10**-17 joule
energy of electron in 2nd state is 5.428 *10**-17 joule

Example number 6.11, Page number 6.25

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

#Variable declaration
m=9.1*10**-31;     #mass of electron(kg)
h=6.626*10**-34;    #planck's constant
lamda=1.66*10**-10;    #wavelength(m)

#Calculation
v=h/(m*lamda);    #velocity(m/s)
KE=(1/2)*m*v**2;    #kinetic energy(eV)

#Result
print "velocity is",int(v/10**3),"km/s"
print "kinetic energy is",round(KE/(1.6*10**-19),2),"eV"

velocity is 4386 km/s
kinetic energy is 54.71 eV

Example number 6.12, Page number 6.25

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

#Variable declaration
V=15000;    #voltage(V)

#Calculation
lamda=12.26/math.sqrt(V);      #de broglie wavelength(angstrom)

#Result
print "de broglie wavelength is",round(lamda,1),"angstrom"

de broglie wavelength is 0.1 angstrom

Example number 6.13, Page number 6.26

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=344;    #voltage(V)
n=1;
theta=60*math.pi/180;    #angle(radian)

#Calculation
lamda=round(12.26/math.sqrt(V),3);      #de broglie wavelength(angstrom)
d=n*lamda/(2*math.sin(theta));    #spacing of crystal(angstrom)

#Result
print "spacing of crystal is",round(d,4),"angstrom"

spacing of crystal is 0.3816 angstrom

Example number 6.14, Page number 6.26

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

#Variable declaration
E=1.5*9.1*10**-31;    #energy(joule)
m=1.676*10**-27;     #mass(kg)
h=6.62*10**-34;    #planck's constant

#Calculation
v=math.sqrt(2*E/m);    
lamda=h/(m*v);       #wavelength(m)

#Result
print "wavelength is",round(lamda*10**6,3),"*10**-6 m"
print "answer varies due to rounding off errors"

wavelength is 9.787 *10**-6 m
answer varies due to rounding off errors