3: Principles of Quantum Mechanics

Example number 3.1, Page number 3.12

In [2]:
#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 = 6.626*10**-34    #planck's constant

#Calculation
v = (1/10)*c      #velocity of proton(m/sec)
lamda = h/(m*v)     #de Broglie wavelength(m)

#Result
print "de Broglie wavelength of proton is",round(lamda/1e-14,3),"*10^-14 m"

de Broglie wavelength of proton is 1.323 *10^-14 m

Example number 3.2, Page number 3.12

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

#Variable declaration
V = 400      #potential(V)

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

#Result
print "de Broglie wavelength of electron is",lamda,"angstrom"

de Broglie wavelength of electron is 0.613 angstrom

Example number 3.3, Page number 3.13

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

#Variable declaration
m = 1.674*10**-27     #mass of neutron(kg)
h = 6.626*10**-34     #planck's constant
e = 1.6*10**-19
KE = 0.025     #kinetic energy(eV)

#Calculation
E = KE*e     #kinetic energy(J)
lamda = h/math.sqrt(2*m*E)      #de Broglie wavelength(m)
lamda_nm = lamda*10**9      #de Broglie wavelength(nm)
lamda_nm = math.ceil(lamda_nm*10**4)/10**4   #rounding off to 4 decimals

#Result
print "de Broglie wavelength is",lamda_nm,"nm" 

de Broglie wavelength is 0.1811 nm

Example number 3.4, Page number 3.14

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

#Variable declaration
V = 1600      #potential(V)

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

#Result
print "de Broglie wavelength of electron is",lamda,"angstrom"

de Broglie wavelength of electron is 0.3065 angstrom

Example number 3.5, Page number 3.18

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

#Variable declaration
delta_x = 0.2      #electron distance(angstrom)
h = 6.626*10**-34    #planck's constant

#Calculation
delta_x = delta_x*10**-10      #electron distance(m)
delta_p = h/(2*math.pi*delta_x)      #uncertainity in momentum(kg.m/s)

#Result
print "uncertainity in momentum is",round(delta_p/1e-24,3),"*10^-24 kg m/s"

 uncertainity in momentum is 5.273 *10^-24 kg m/s

Example number 3.6, Page number 3.27

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

#Variable declaration
n1 = 1
n2 = 1
n3 = 1      #for lowest energy
e = 1.6*10**-19
h = 6.62*10**-34      #planck's constant
m = 9.1*10**-31      #mass of electron(kg)
L = 0.1     #side of box(nm)

#Calculation
L = L*10**-9    #side of box(m)
E1 = h**2*(n1**2+n2**2+n3**2)/(8*m*L**2)      #lowest energy(J)
E1 = E1/e      #lowest energy(eV)
E1 = math.ceil(E1*10)/10    #rounding off to 1 decimal

#Result
print "lowest energy of electron is",E1,"eV"

lowest energy of electron is 112.9 eV

Example number 3.7, Page number 3.27

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

#Variable declaration
n1 = 1
n2 = 1
n3 = 2      #for level next to the lowest
e = 1.6*10**-19
h = 6.62*10**-34      #planck's constant
m = 9.1*10**-31       #mass of electron(kg)
L = 0.1     #side of box(nm)

#Calculation
L = L*10**-9    #side of box(m)
E1 = h**2*(n1**2+n2**2+n3**2)/(8*m*L**2)      #lowest energy(J)
E1 = E1/e      #lowest energy(eV)
E1 = math.ceil(E1*10**2)/10**2    #rounding off to 2 decimals

#Result
print "energy of electron is",E1,"eV"

energy of electron is 225.75 eV

Example number 3.8, Page number 3.28

In [11]:
#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 = 1.6*10**-19
E = 2000     #energy(eV)

#Calculation
E = E*e      #energy(J)
lamda = h/math.sqrt(2*m*E)      #wavelength(m)
lamda_nm = lamda*10**9      #velength(nm)
lamda_nm = math.ceil(lamda_nm*10**4)/10**4    #rounding off to 4 decimals

#Result
print "wavelength is",lamda_nm,"nm"

wavelength is 0.0275 nm

Example number 3.9, Page number 3.28

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

#Variable declaration
n = 1     #for minimum energy
h = 6.626*10**-34      #planck's constant(J sec)
m = 9.91*10**-31      #mass of electron(kg)
L = 4*10**-10     #side of box(m)

#Calculation
E1 = ((h**2)*(n**2))/(8*m*(L**2))      #lowest energy(J)
E1 = E1*10**18;
E1 = math.ceil(E1*10**4)/10**4    #rounding off to 4 decimals

#Result
print "energy of electron is",E1,"*10**-18 J"

energy of electron is 0.3462 *10**-18 J

Example number 3.10, Page number 3.29

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1 = 1     #for ground state
n2 = 2     #for 1st excited state
n3 = 3     #for 2nd excited state
h = 6.626*10**-34      #planck's constant(J sec)
m = 9.1*10**-31      #mass of electron(kg)
L = 1*10**-10       #width(m)

#Calculation
E1 = h**2*n1**2/(8*m*L**2)      #energy in ground state(J)
E2 = n2**2*E1       #energy in 1st excited state(J)
E3 = n3**2*E1       #energy in 2nd excited state(J)

#Result
print "energy in ground state is",round(E1/1e-18,3),"*10^-18 J"
print "energy in 1st excited state is",round(E2/1e-17,3),"*10^-17 J"
print "energy in 2nd excited state is",round(E3/1e-17,3),"*10^-17 J"

energy in ground state is 6.031 *10^-18 J
energy in 1st excited state is 2.412 *10^-17 J
energy in 2nd excited state is 5.428 *10^-17 J

Example number 3.11, Page number 3.30

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

#Variable declaration
h = 6.626*10**-34      #planck's constant(J sec)
m = 9.1*10**-31      #mass of electron(kg)
e = 1.6*10**-19
lamda = 1.66*10**-10     #wavelength(m)

#Calculation
v = h/(m*lamda)      #velocity of electron(m/sec)
v_km = v*10**-3      #velocity of electron(km/sec)
KE = (1/2)*m*v**2    #kinetic energy(J)
KE_eV = KE/e        #kinetic energy(eV)
KE_eV = math.ceil(KE_eV*10**3)/10**3    #rounding off to 3 decimals

#Result
print "velocity of electron is",int(v_km),"km/sec"
print "kinetic energy of electron is",KE_eV,"eV"

velocity of electron is 4386 km/sec
kinetic energy of electron is 54.714 eV

Example number 3.12, Page number 3.31

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

#Variable declaration
V = 15      #potential(kV)

#Calculation
V = V*10**3     #potential(V)
lamda = 12.26/math.sqrt(V)      #de Broglie wavelength(angstrom)
lamda = math.ceil(lamda*100)/100    #rounding off to 2 decimals

#Result
print "wavelength of electron waves is",lamda,"angstrom"

wavelength of electron waves is 0.11 angstrom

Example number 3.13, Page number 3.31

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
V = 344      #potential(V)
n = 1     #for 1st reflection maximum
theta = 60     #glancing angle(degrees)

#Calculation
lamda = 12.26/math.sqrt(V)      #de Broglie wavelength(angstrom)
lamda_m = lamda*10**-10     #de Broglie wavelength(m)
theta = theta*math.pi/180     ##glancing angle(radians)
d = n*lamda_m/(2*math.sin(theta))      #interatomic spacing(m)
d = d*10**10       #interatomic spacing(angstrom)
d = math.ceil(d*10**5)/10**5    #rounding off to 5 decimals

#Result
print "interatomic spacing of crystal is",d,"angstrom"

interatomic spacing of crystal is 0.38164 angstrom