# 5: Quantum Theory¶

## Example number 5.1, Page number 97¶

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

#Variable declaration
W1=4;     #wavelength(Angstrom)
W2=1;     #wavelength(Angstrom)
e=1.6*10**-19;   #the charge on electron(C)
m=9.12*10**-31;   #mass of electron(kg)

#Calculation
E=12400/W1;      #energy(eV)
v=math.sqrt(E*e*2/m);      #velocity(m/s)
E1=12400/W2;       #energy(eV)
v1=math.sqrt(E1*e*2/m);        #velocity(m/s)

#Result
print "The energy for 4 angstrom wavelength is",E,"eV"
print "The velocity is",round(v/1e+6),"*10**6 m/s"
print "The energy for 1 angstrom wavelength is",E1,"eV"
print "The velocity is",round(v1/1e+6),"*10**6 m/s"

#answers given in the book are wrong

The energy for 4 angstrom wavelength is 3100.0 eV
The velocity is 33.0 *10**6 m/s
The energy for 1 angstrom wavelength is 12400.0 eV
The velocity is 66.0 *10**6 m/s


## Example number 5.2, Page number 98¶

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

#Variable declaration
f=880*10**3;      #frequency(Hz)
P=10*10**3;    #Power(W)
h=6.625*10**-34;    #Plank's constant

#Calculation
E=h*f;    #energy carried by each photon(J)
n=P/E;    #number of photons emitted per second

#Result
print "The number of photons emitted per second are",round(n/1e+30,2),"*10**30"

The number of photons emitted per second are 17.15 *10**30


## Example number 5.3, Page number 98¶

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

#Variable declaration
P=200;     #power(W)
W=6123*10**-10;    #wavelength(m)
c=3*10**8;   #speed of light(m/s)
h=6.625*10**-34;    #Plank's constant

#Calculation
E=h*c/W;     #energy content(J)
n=2/E;      #number of quanta emitted per second

#Result
print "Number of quanta emitted per second is",round(n/1e+18,2),"*10**18"

Number of quanta emitted per second is 6.16 *10**18


## Example number 5.4, Page number 98¶

In [16]:
#import modules
import math
from __future__ import division

#Variable declaration
N=5*10**4;      #no. of photons
W=3000*10**-10;    #wavelength(m)
J=5*10**-3;    #senstivity(A/W)
h=6.625*10**-34;    #Plank's constant
c=3*10**8;       #speed of light(m/s)
e=1.6*10**-19;       #the charge on electron(C)

#Calculation
E=h*c/W;  #energy content of each photon(J)
TE=N*E;   #total energy(J)
I=J*TE;   #current produced(ampere)
n=I/e;       #number of photo electrons ejected

#Result
print "number of photoelectrons emitted are",int(n)
print "answer given in the book varies due to rounding off errors"

number of photoelectrons emitted are 1035
answer given in the book varies due to rounding off errors


## Example number 5.5, Page number 99¶

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

#Variable declaration
W=5*10**-7;     #wavelength(m)
F=10**-5;    #force(N)
h=6.625*10**-34;    #Plank's constant
m=1.5*10**-3;     #mass(kg)
c=3*10**8;     #speed of light in (m/s)
S=0.1;     #specific heat

#Calculation
n=F*W/h;    #number of photons
E=F*c/4200;     #energy of each photon(kcal/s)
theta=E/(m*S);     #rate of rise in temperature(C/s)

#Result
print "number of photons are",round(n/1e+21,3),"*10**21"
print "the rate of temperature rise is",round(theta/1e+3,1),"*10**3 C/s"

number of photons are 7.547 *10**21
the rate of temperature rise is 4.8 *10**3 C/s


## Example number 5.6, Page number 99¶

In [30]:
#import modules
import math
from __future__ import division

#Variable declaration
W=4500*10**-10;    #wavelength(m)
V=150;   #rated voltage(W)
h=6.625*10**-34;   #Plank's constant
c=3*10**8;      #speed of light(m/s)

#Calculation
P=V*8/100;     #lamp power emitted(W)
E=h*c/W;       #energy carried by 1 photon(J)
n=P/E;        #number of photons emitted per second

#Result
print "Number of photons emitted per second is",round(n/1e+18,2),"*10**18"
print "answer given in the book varies due to rounding off errors"

Number of photons emitted per second is 27.17 *10**18
answer given in the book varies due to rounding off errors


## Example number 5.7, Page number 99¶

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

#Variable declaration
f=1*10**12;     #frequency(Hz)
h=6.625*10**-34;    #Plank's constant

#Calculation
E=h*f;     #energy per photon(J)
n=E/6.625;     #number of photons

#Result
print "the number of photons required is",n

the number of photons required is 1e-22


## Example number 5.8, Page number 100¶

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

#Variable declaration
W=5200*10**-10;     #wavelength(m)
h=6.625*10**-34;    #Plank's constant
m=9.12*10**-31;     #mass of electron(kg)

#Calculation
p=h/W;      #momentum(kg-m/s)
v=p/m;      #velocity(m/s)

#Result
print "velocity is",round(v),"m/s"
print "answer given in the book varies due to rounding off errors"

velocity is 1397.0 m/s
answer given in the book varies due to rounding off errors


## Example number 5.9, Page number 105¶

In [37]:
#import modules
import math
from __future__ import division

#Variable declaration
v=7*10**5;    #maximum speed(m/sec)
f=8*10**14;   #frequency(Hz)
h=6.625*10**-34;    #Plank's constant
c=3*10**8;       #speed of light(m/s)
m=9.12*10**-31;  #mass of electron(kg)

#Calulation
E=m*v*v/2;    #energy(J)
fo=f-(E/h);    #threshold frequency of the surface(Hz)

#Result
print "the threshold frequency is",round(fo/1e+14,2),"*10**14 Hz"

the threshold frequency is 4.63 *10**14 Hz


## Example number 5.10, Page number 106¶

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

#Variable declaration
Wo=2300*10;    #threshold wavelength(Angstrom)
W=1800*10;     #incident light wavelength(Angstrom)

#Calculation
w=124000/Wo;      #maximum energy of photoelectrons emitted(eV)
E=124000*((1/W)-(1/Wo));    #work function for tungsten(eV)

#Result
print "maximum energy of photoelectrons emitted is",round(w,1),"eV"
print "work function for tungsten is",round(E,1),"eV"

maximum energy of photoelectrons emitted is 5.4 eV
work function for tungsten is 1.5 eV


## Example number 5.11, Page number 106¶

In [43]:
#import modules
import math
from __future__ import division

#Variable declaration
W=6000;      #wavelegth(Angstrom)
v=4*10**5;      #velocity(m/sec)
m=9.12*10**-31;    #mass of electron(kg)
e=1.6*10**-19;     #the charge on electron(C)

#Calculation
KE=m*v**2/(2*e);     #kinetic energy of photo electronns(eV)
WF=12400/W;          #energy content of photon(eV)
Wo=12400/(WF-KE);     #photo electric threshold wavelength(angstrom)

#Result
print "The Kinetic energy is",KE,"eV"
print "The threshold wavelength is",int(Wo),"Angstrom"
print "answer given in the book varies due to rounding off errors"

The Kinetic energy is 0.456 eV
The threshold wavelength is 7698 Angstrom
answer given in the book varies due to rounding off errors


## Example number 5.12, Page number 106¶

In [46]:
#import modules
import math
from __future__ import division

#Variable declaration
Wo=4.8;    #work function(eV)
W=2220;    #wavelength(angstrom)

#Calculation
E=12400/W;    #energy of light photon(eV)
Emax=E-Wo;    #maximum kinetic energy(eV)

#Result
print "maximum kinetic energy is",round(Emax,3),"eV"

maximum kinetic energy is 0.786 eV


## Example number 5.13, Page number 106¶

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

#Variable declaration
W=4000*10**-10;     #wavelength(m)
Vs=0.4;     #retarding potential(eV)
h=6.625*10**-34;    #Plank's constant
c=3*10**8;      #speed of light(m/s)
e=1.6*10**-19;     #the charge on electron(C)

#Calculation
f=c/W;    #frequency of light(Hz)
E=h*f/e;    #photon energy(eV)
Wo=E-Vs;    #work function(eV)
fo=Wo/h*e;     #threshold frequency(Hz)
NE=(E-Wo)*e;    #net energy(J)

#Result
print "The light frequency is",f,"Hz"
print "The photon energy is",round(E,1),"eV"
print "The work function is",round(Wo,1),"eV"
print "The threshold frequency is",round(fo/1e+14,1),"*10**14 Hz"
print "The net energy is",NE,"J"

The light frequency is 7.5e+14 Hz
The photon energy is 3.1 eV
The work function is 2.7 eV
The threshold frequency is 6.5 *10**14 Hz
The net energy is 6.4e-20 J


## Example number 5.14, Page number 107¶

In [57]:
#import modules
import math
from __future__ import division

#Variable declaration
W1=3310*10**-10;    #photon wavelength(m)
W2=5000*10**-10;    #photon wavelength(m)
E1=3*10**-19;     #electron energy(J)
E2=0.972*10**-19;   #electron energy(J)
c=3*10**8;       #speed of light in m/s

#Calculation
h=(E1-E2)*(W1*W2)/(c*(W2-W1));    #planck's constant(Js)
Wo=c*h/E1;        #threshold wavelength(m)

#Result
print "the plancks const is",round(h/1e-34,2),"*10**-34 Js"
print "The threshold wavelength is",round(Wo*1e+10),"*10**-10 m"
print "answer given in the book is wrong"

the plancks const is 6.62 *10**-34 Js
The threshold wavelength is 6620.0 *10**-10 m
answer given in the book is wrong


## Example number 5.15, Page number 107¶

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

#Variable declaration
W=6525;     #wavelength(angstrom)

#Calculation
Vo_a=12400*((1/4000)-(1/W));       #stopping potential(V)
Vo_b=12400*((1/2000)-(1/W));       #stopping potential(V)
Vo_c=12400*((1/2000)-(2/W));       #stopping potential(V)

#Result
print "Stopping potential is",round(Vo_a,1),"Volt"
print "Stopping potential is",round(Vo_b,1),"Volt"
print "Stopping potential is",round(Vo_c,1),"Volt"

Stopping potential is 1.2 Volt
Stopping potential is 4.3 Volt
Stopping potential is 2.4 Volt


## Example number 5.16, Page number 107¶

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

#Variable declaration
Wo=5000;      #wavelength(angstrom)
V=3.1;        #stopping potential(V)

#Calcultion
W=1/((V/12400)+(1/Wo));      #wavelength(angstrom)

#Result
print "The wavelength is",int(W),"Angstrom"

The wavelength is 2222 Angstrom


## Example number 5.17, Page number 108¶

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

#Variable declaration
W=2000;         #wavelength(Angstrom)
Vs=4.2;         #Work Function(eV)
e=1.6*10**-19;      #the charge on electron(C)

#Calculation
E=12400/W;       #photon energy(eV)
Emax=(E-Vs)*e;     #maximum kinetic energy(J)
Emin=0;         #minimum kinetic energy
Vo=Emax/e;      #stopping potential(V)
Wo=12400/Vs;      #cut off wavelength(angstrom)

#Result
print "Kinetic Energy of fastest photoelectron is",Emax,"J"
print "Kinetic Energy of slowest moving electron is",Emin,"J"
print "Stopping potential is",Vo,"V"
print "The cutoff wavelength is",round(Wo,1),"Angstrom"

Kinetic Energy of fastest photoelectron is 3.2e-19 J
Kinetic Energy of slowest moving electron is 0 J
Stopping potential is 2.0 V
The cutoff wavelength is 2952.4 Angstrom


## Example number 5.18, Page number 108¶

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

#Variable declaration
Vs1=4.6;     #Stopping Potential(V)
Vs2=12.9;    #Stopping Potential(V)
f1=2*10**15;     #frequency(Hz)
f2=4*10**15;     #frequency(Hz)
e=1.6*10**-19;   #the charge on electron(C)

#Calculation
h=((Vs2-Vs1)*e)/(f2-f1);     #planck's constant(Js)

#Result
print "The Planck's constant is",h,"Js"
print "answer given in the book is wrong"

The Planck's constant is 6.64e-34 Js
answer given in the book is wrong