5: Uncertainity Principle

Example number 1, Page number 177

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration  
h=6.6*10**-34;      #plancks constant(J s)
deltax=4*10**-10;   #uncertainity(m)

#Calculations
delta_px=h/deltax;    #uncertainity in momentum(kg m/sec)

#Result
print "uncertainity in momentum is",delta_px,"kg m/sec"

uncertainity in momentum is 1.65e-24 kg m/sec

Example number 2, Page number 177

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

#Variable declaration  
h=6.6*10**-34;      #plancks constant(J s)
m=9.1*10**-31;      #mass(kg)
v=600;              #speed(m/s)
deltapx=(0.005/100)*m*v;  #uncertainity in momentum(kg m/sec)

#Calculations
deltax=h/deltapx;    #uncertainity in position(m)

#Result
print "uncertainity in position is",round(deltax,5),"m"
print "answer given in the book is wrong"

uncertainity in position is 0.02418 m
answer given in the book is wrong

Example number 3, Page number 177

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

#Variable declaration  
h=6.63*10**-34;      #plancks constant(J s)
deltax=0.1*10**-10;   #uncertainity(m)
m0=9.1*10**-31;      #mass(kg)

#Calculations
deltap=h/deltax;    #uncertainity in momentum(kg m/sec)
deltav=deltap/m0;   #uncertainity in velocity(m/sec) 

#Result
print "uncertainity in momentum is",deltap,"kg m/sec"
print "uncertainity in velocity is",round(deltav/10**7,3),"*10**7 m/sec"

uncertainity in momentum is 6.63e-23 kg m/sec
uncertainity in velocity is 7.286 *10**7 m/sec

Example number 4, Page number 178

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

#Variable declaration  
me=9.1*10**-31;      #mass of electron(kg)
mp=1.67*10**-27;      #mass of proton(kg)

#Calculations
deltavebydeltavp=mp/me;    #uncertainity in velocity

#Result
print "uncertainity in velocity is",int(deltavebydeltavp)

uncertainity in velocity is 1835

Example number 5, Page number 178

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
v=3*10**7;           #velocity(m/sec)
c=3*10**8;           #velocity of light(m/sec)
m0=9*10**-31;        #mass(kg)

#Calculations
deltaxmin=h*math.sqrt(1-(v**2/c**2))/(2*math.pi*m0*v);   #smallest possible uncertainity in position(m)

#Result
print "smallest possible uncertainity in position is",round(deltaxmin*10**10,4),"angstrom"

smallest possible uncertainity in position is 0.0388 angstrom

Example number 6, Page number 179

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration  
h=6.6*10**-34;      #plancks constant(J s)
deltapmax=10**-9;   #uncertainity in momentum(kg m/sec)
m=9*10**-31;        #mass(kg)

#Calculations
deltapmin=h/deltapmax;   #smallest possible uncertainity in momentum(kg m/sec)
deltavxmin=deltapmin/m;  #minimum uncertainity in velocity(m/s) 

#Result
print "minimum uncertainity in velocity is",round(deltavxmin/10**5,1),"*10**5 m/s"

minimum uncertainity in velocity is 7.3 *10**5 m/s

Example number 7, Page number 179

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

#Variable declaration  
c=3*10**8;           #velocity of light(m/sec)
lamda=6000*10**-10;  #wavelength(m)
dlamda=10**-4*10**-10;    #width(m)

#Calculations
deltat=lamda**2/(2*math.pi*c*dlamda);     #time required(second)

#Result
print "time required is",round(deltat*10**8,1),"*10**-8 second"

time required is 1.9 *10**-8 second

Example number 8, Page number 180

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

#Variable declaration  
h=6.63*10**-34;      #plancks constant(J s)
m=9.1*10**-31;      #mass(kg)
v=3.5*10**5;              #speed(m/s)
deltap=(0.0098/100)*m*v;  #uncertainity in momentum(kg m/sec)

#Calculations
deltax=h/(2*math.pi*deltap);    #uncertainity in position(m)

#Result
print "uncertainity in position is",round(deltax*10**6,3),"*10**-6 m"
print "answer given in the book varies due to rounding off errors"

uncertainity in position is 3.381 *10**-6 m
answer given in the book varies due to rounding off errors

Example number 9, Page number 180

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

#Variable declaration  
h=6.63*10**-34;      #plancks constant(J s)
m0=9.1*10**-31;      #mass(kg)
deltax=2*10**-15;    #uncertainity in position(m)
e=1.6*10**-19;       #charge(coulomb)

#Calculations
deltap=h/(2*math.pi*deltax);    #uncertainity in momentum(kg m/sec)
K=deltap**2/(2*m0*e);           #kinetic energy of electron(eV)

#Result
print "uncertainity in momentum is",round(deltap*10**20,3),"*10**-20 kg m/sec"
print "kinetic energy of electron is",round(K/10**6,1),"MeV"
print "answer for kinetic energy given in the book is wrong"

uncertainity in momentum is 5.276 *10**-20 kg m/sec
kinetic energy of electron is 9559.1 MeV
answer for kinetic energy given in the book is wrong

Example number 10, Page number 180

In [35]:
#importing modules
import math
from __future__ import division

#Variable declaration  
chi=1.05*10**-34;      #plancks constant(J s)
deltaxmax=2*5*10**-15; #uncertainity in momentum(kg m/sec)
m=1.67*10**-27;        #mass(kg)
e=1.6*10**-19;       #charge(coulomb)

#Calculations
deltapmin=chi/deltaxmax;      #minimum uncertainity in momentum(kg m/sec)
Emin=deltapmin**2/(2*m*e);      #minimum kinetic energy(eV)

#Result
print "minimum uncertainity in momentum is",deltapmin,"kg m/sec"
print "minimum kinetic energy is",round(Emin/10**5,2),"*10**5 eV"

minimum uncertainity in momentum is 1.05e-20 kg m/sec
minimum kinetic energy is 2.06 *10**5 eV

Example number 11, Page number 181

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

#Variable declaration  
e=5/100;           #error
h=1;               #assume

#Calculations
deltaJ=e*2*h;      #uncertainity in angular momentum
delta_theta=h/deltaJ;     #angular orbital position(radian)

#Result
print "angular orbital position is",int(delta_theta),"radian"

angular orbital position is 10 radian