Quantum Physics

Example number 4.1, Page number 117

In [1]:
#To calculate the energy and momentum of photon

#importing modules
import math

#Variable declaration
c = 3*10**8;       #velocity of light(m/sec)
h = 6.62*10**-34;     #planck's constant
lamda = 1.2;          #wavelength of photon(Angstrom)
e = 1.6*10**-19;      #conversion factor from J to eV

#Calculation
lamda = lamda*10**-10;       #wavelength of photon(m)
E = (h*c)/(lamda*e);         #energy of photon(eV)
E=math.ceil(E*10)/10;   #rounding off to 1 decimal
p = h/lamda;            #momentum of photon(kg m/s)

#Result
print "energy of the photon is",E,"eV"
print "momentum of the photon is",p,"kg m/s"

energy of the photon is 10343.8 eV
momentum of the photon is 5.51666666667e-24 kg m/s

Example number 4.2, Page number 117

In [2]:
#To calculate the number of photons emitted 

#importing modules
import math

#Variable declaration
h = 6.625*10**-34;     #planck's constant
new = 900;             #frequency(kHz)
E1 = 10;               #power radiated(kW)

#Calculation
E1 = E1*10**3;         #power radiated(W)
new = new*10**3;       #frequency(Hz)
E = h*new;         #energy of photon(J)
N = E1/E;          #number of photons emitted 

#Result
print "number of photons emitted per second is",N

number of photons emitted per second is 1.67714884696e+31

Example number 4.3, Page number 118

In [4]:
#To calculate the number of photons emitted 

#importing modules
import math

#Variable declaration
c = 3*10**8;       #velocity of light(m/sec)
h = 6.63*10**-34;     #planck's constant
lamda = 5893;         #wavelength of photon(Angstrom)
E1 = 100;             #power of lamp(W) 

#Calculation
lamda = lamda*10**-10;       #wavelength of photon(m)
E = h*c/lamda;         #energy of photon(J)
N = E1/E;          #number of photons emitted 

#Result
print "number of photons emitted per second is",N
print "answer given in the book is wrong"

number of photons emitted per second is 2.96279537456e+20
answer given in the book is wrong

Example number 4.4, Page number 118

In [5]:
#To calculate the wavelength of scattered radiation

#importing modules
import math

#Variable declaration
c = 3*10**8;       #velocity of light(m/sec)
h = 6.6*10**-34;     #planck's constant
m0 = 9.1*10**-31;        #mass of photon(kg)
theta = 30;              #viewing angle(degrees)
lamda = 2.8*10**-10;         #wavelength of photon(m)

#Calculation
x = math.pi/180;       #conversion factor from degrees to radians
theta = theta*x;       #viewing angle(radian) 
lamda_dash = (2*h*(math.sin(theta/2))**2/(m0*c))+lamda;        #wavelength of scattered radiation(m)
lamda_dash = lamda_dash*10**10;           #wavelength of scattered radiation(Angstrom)
lamda_dash=math.ceil(lamda_dash*10**5)/10**5;   #rounding off to 5 decimals

#Result
print "wavelength of scattered radiation is",lamda_dash,"Angstrom"

wavelength of scattered radiation is 2.80324 Angstrom

Example number 4.5, Page number 119

In [6]:
#To calculate the deBroglie wavelength

#importing modules
import math

#Variable declaration
h = 6.6*10**-34;     #planck's constant
m = 0.040;        #mass of bullet(kg)
v = 1;            #speed of bullet(km/s)

#Calculation
v = v*10**3;      #speed of bullet(m/s)
p = m*v;          #momemtun of bullet(kg m/s)
lamda = h/p;      #deBroglie wavelength(m)
lamda = lamda*10**10;     #deBroglie wavelength(Angstrom)

#Result
print "deBroglie wavelength is",lamda,"Angstrom"

deBroglie wavelength is 1.65e-25 Angstrom

Example number 4.6, Page number 119

In [8]:
#To calculate the energy of particle

#importing modules
import math

#Variable declaration
n = 1;               #lowest energy state
a = 0.1;             #width of box(nm)
h = 6.625*10**-34;     #planck's constant
e = 1.602*10**-19;       #conversion factor from J to eV
m = 9.11*10**-31;        #mass of particle(kg)

#Calculation
a = a*10**-9;        #width of box(m)
E = (n**2)*(h**2)/(8*m*(a**2));      #energy of particle(J)
E_eV = E/e;             #energy of particle(eV)
E_eV=math.ceil(E_eV*10)/10;   #rounding off to 1 decimal

#Result
print "energy of particle is",E,"J or",E_eV,"eV" 

energy of particle is 6.02231407794e-18 J or 37.6 eV

Example number 4.7, Page number 120

In [9]:
#To calculate the minimum energy of an electron

#importing modules
import math

#Variable declaration
n = 1;               #lowest energy state
a = 4;             #width of well(nm)
h = 6.625*10**-34;     #planck's constant
e = 1.6025*10**-19;       #conversion factor from J to eV
m = 9.11*10**-31;        #mass of electron(kg)

#Calculation
a = a*10**-9;        #width of box(m)
E = (n**2)*(h**2)/(8*m*(a**2));      #energy of particle(J)
E_eV = E/e;             #energy of particle(eV)
E_eV=math.ceil(E_eV*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "minimum energy of electron is",E,"J or",E_eV,"eV" 

minimum energy of electron is 3.76394629871e-21 J or 0.0235 eV

Example number 4.8, Page number 120

In [11]:
#To calculate the energy required to excite the electron

#importing modules
import math

#Variable declaration
n1 = 1;               #lowest energy state
n2 = 6;               #for 6th excited state
a = 0.1;             #width of box(nm)
h = 6.625*10**-34;     #planck's constant
e = 1.602*10**-19;       #conversion factor from J to eV
m = 9.11*10**-31;        #mass of electron(kg)

#Calculation
a = a*10**-9;        #width of box(m)
E1 = (n1**2)*(h**2)/(8*m*(a**2));      #energy of electron in ground state(J)
E6 = (n2**2)*(h**2)/(8*m*(a**2));      #energy of electron in excited state(J)
E = E6-E1;                          #energy required to excite the electron(J)
E_eV = E/e;             #energy required to excite the electron(eV)
E_eV=math.ceil(E_eV*10)/10;   #rounding off to 1 decimal

#Result
print "energy required to excite the electron is",E,"J or",E_eV,"eV" 
print "answer for energy in eV given in the book is wrong"

energy required to excite the electron is 2.10780992728e-16 J or 1315.8 eV
answer for energy in eV given in the book is wrong

Example number 4.9, Page number 121

In [12]:
#To calculate the change in wavelength

#importing modules
import math

#Variable declaration
h = 6.625*10**-34;     #planck's constant
c = 3*10**8;       #velocity of light(m/sec)
m0 = 9.11*10**-31;        #rest mass of electron(kg)
phi = 90;              #angle of scattering(degrees)
x = math.pi/180;       #conversion factor from degrees to radians

#Calculation
phi = phi*x;           ##angle of scattering(radian)
delta_lamda = h*(1-math.cos(phi))/(m0*c);         #change in wavelength(m)

#Result
print "change in wavelength of X-ray photon is",delta_lamda,"m"

change in wavelength of X-ray photon is 2.42407610684e-12 m
In [ ]: