9: Quantum Theory

Example number 9.1, Page number 171

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

#Variable declaration
r=0.05;                  #radius of the wire(mm)
l=4;                     #length of the wire(cm)
e=1;
T=3000;                  #temperature(K)
s=5.6703*10**-8;         #stefan's constant 

#Calculation  
A=2*math.pi*r*l*10**-5;      #area(m**2)
p=s*T**4*A*e;            #power radiated by the filament(W)

#Result
print "The power radiated by the filament is",round(p,2),"W"
print "answer given in the book is wrong"
The power radiated by the filament is 57.72 W
answer given in the book is wrong

Example number 9.2, Page number 171

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                   #plancks constant
c=3*10**8;                         #speed of light(m/s)
lamda=550;                        #wavelength(nm)

#Calculation                        
E=(h*c)/(lamda*10**-9);           #energy of photon(J)
Es=0.1/E;                          #number of photons(per square cm per second)

#Result
print "The number of photons are",round(Es/10**17,2),"*10**17 per square cm per second"
print "answer in the book varies due to rounding off errors"
The number of photons are 2.77 *10**17 per square cm per second
answer in the book varies due to rounding off errors

Example number 9.3, Page number 171

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

#Variable declaration
h=6.626*10**-34;                      #plancks constant
c=3*10**8;                            #speed of light(m/s)
lamda=300*10**-9;                    #wavelength(m)
e=1.6*10**-19;
phi=2.2;                              #work function(eV)

#Calculation                        
E=(h*c)/lamda;                       #energy of photon(J)
Kmax=(E-(phi*e))/e;                           #maximum kinetic energy(eV)

#Result
print "The maximum kinetic energy  is",round(Kmax,2),"eV"
The maximum kinetic energy  is 1.94 eV

Example number 9.4, Page number 172

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

#Variable declaration
h=6.626*10**-34;                      #plancks constant
c=3*10**8;                            #speed of light(m/s)
lamda=175*10**-9;                    #wavelength of light(m)
w=5;                                  #work function of nickel(eV)

#Calculation                        
E=(h*c)/(lamda*1.6*10**-19);         #Energy of 200 nm photon(eV)
#From photoelectric equation E-w is the potential difference
p=E-w;                                #potential difference required to stop the fastest electron(eV)

#Result
print "The potential difference that should be applied is",round(p,1),"V"
The potential difference that should be applied is 2.1 V

Example number 9.5, Page number 172

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                   #plancks constant
c=3*10**8;                         #speed of light(m/s)
e=1.6*10**-19;
V=50;                              #accelerating voltage(kV)

#Calculation                        
lambdamin=((h*c)/(e*V*10**3))*10**9;      #shortest wavelength of X-rays(nm)

#Result
print "The shortest wavelength of X-rays is",round(lambdamin,4),"nm"
The shortest wavelength of X-rays is 0.0248 nm

Example number 9.6, Page number 172

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
lambda1=0.708;                  #wavelength of a certain line in an X-ray spectrum(angstrom)
Z1=42;                          #atomic number
Z2=24;
a=1;                            #screening constant

#Calculation                        
lambda2=(lambda1*(Z1-a)**2)/((Z2-a)**2);      #wavelength of same line(angstrom)

#Result
print "The wavelength of same line is",round(lambda2,2),"angstrom"
The wavelength of same line is 2.25 angstrom

Example number 9.7, Page number 172

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
#From Bragg's law 2*d*sin(teta)=n*lambda
n=1;
lamda=0.32;                    #wavelength(nm)
theta=28;                       #angle at which first order Bragg's reflection is observed(degrees)

#Calculation                        
theta=theta*math.pi/180;        #angle(radian)
d=lamda/(2*math.sin(theta));      #distance between atomic planes(nm)

#Result
print "The distance between atomic planes is",round(d,2),"nm"
The distance between atomic planes is 0.34 nm

Example number 9.8, Page number 172

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

#Variable declaration
h=6.626*10**-34;                   #plancks constant
theta=50;                   #angle(degrees)
m=9.1*10**-31;              #mass of electron(kg)
c=3*10**8;                  #speed of light(m/s)

#Calculation                        
theta=theta*math.pi/180;    #angle(radian)
deltalambda=(h/(m*c))*(1-math.cos(theta))*10**12;      
lambdafin=2.5;              #wavelength of scattered X-rays
lambdainit=lambdafin-deltalambda;     #wavelength of X-rays in the incident beam(pm)

#Result
print "The wavelength of X-rays in the incident beam is",round(lambdainit,2),"pm"
The wavelength of X-rays in the incident beam is 1.63 pm

Example number 9.9, Page number 172

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                 #plancks constant
c=3*10**8;                       #speed of light(m/s)
lamda=500*10**-9;               #wavelength of laser(m)
t=20*10**-3;                     #time(s)
N=2.52*10**16;                   #number of photons in a 20ms pulse

#Calculation                        
E=(h*c)/lamda;                  #Energy of 500 nm photon(J)
p=E*N/t;                         #power of the laser(W)

#Result
print "The power of the laser is",round(p,1),"W"
The power of the laser is 0.5 W

Example number 9.10, Page number 173

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                        #plancks constant
c=3*10**8;                              #speed of light(m/s)
lamda=350*10**-9;                      #threshold wavelength(m)
e=1.6*10**-19;

#Calculation  
W=h*c/(lamda*e);             #work function of the surface(eV)

#Result
print "The work function of the surface is",round(W,2),"eV"
The work function of the surface is 3.55 eV

Example number 9.11, Page number 173

In [42]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                  #plancks constant
c=3*10**8;                        #speed of light(m/s)
e=1.6*10**-19;
lambdamin=0.02*10**-9;            #minimum wavelength(m)

#Calculation                        
V=(h*c/(lambdamin*e))*10**-3;       #accelerating voltage(kV)

#Result
print "The accelerating voltage needed to produce minimum wavelength is",round(V,4),"kV"
The accelerating voltage needed to produce minimum wavelength is 62.1187 kV

Example number 9.12, Page number 173

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration
#According to Bragg's eq.2*d*sin(teta)=n*lambda
n=2;                     #since second order Bragg's eq.
d=5;                     #since d=5(lambda)
lamda=1;

#Calculation                        
a=(n*lamda)/(2*5*lamda);
theta=math.asin(a);      #angle of second order Braggs reflection(radian)
theta=theta*180/math.pi;      #angle(degrees)

#Result
print "The angle of second order Braggs reflection is",round(theta,2),"degrees"
The angle of second order Braggs reflection is 11.54 degrees

Example number 9.13, Page number 173

In [49]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;                     #plancks constant
c=3*10**8;                           #speed of light(m/s)
lamda=0.03;                         #wavelength(nm)
p=80/100;

#Calculation                        
E=(h*c)/(lamda*10**-9);             #energy of photon(J) 
TE=E/p;                              #Total energy.E=80% of TE(J)
TE=TE*(10**-3)/e;                    #Total energy(keV)

#Result
print "The electron must have been accelerated through a potential difference of",round(TE,3),"kV" 
The electron must have been accelerated through a potential difference of 51.766 kV