5: Uncertainity Principle

Example number 1, Page number 180

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

#Variable declaration  
hby2pi=1.055*10**-34;      #plancks constant(J s)
deltax=5*10**-14;          #uncertainity(m)

#Calculations
delta_px=hby2pi/deltax;    #uncertainity in momentum(kg m/sec)

#Result
print "uncertainity in momentum is",delta_px*10**20,"*10**-20 kg m/sec"

uncertainity in momentum is 0.211 *10**-20 kg m/sec

Example number 2, Page number 180

In [6]:
#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)
deltap=(0.005/100)*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**3,2),"*10**-3 m"

uncertainity in position is 3.85 *10**-3 m

Example number 3, Page number 180

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltax=3*10**-11;    #uncertainity(m)

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

#Result
print "uncertainity in momentum is",round(deltap*10**24,1),"*10**-24 kg ms-1"

uncertainity in momentum is 3.5 *10**-24 kg ms-1

Example number 4, Page number 180

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltat=10**-8;       #lifetime of excited atom(sec)
e=1.6*10**-19;       #charge(coulomb)

#Calculations
deltaE=h/(2*math.pi*deltat*e);    #uncertainity in determination of energy(eV)

#Result
print "uncertainity in determination of energy is",round(deltaE*10**8,2),"*10**-8 eV"

uncertainity in determination of energy is 6.59 *10**-8 eV

Example number 5, Page number 181

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltaphi=math.pi/(180*60*60);      

#Calculations
deltaL=h/(2*math.pi*deltaphi);    #uncertainity in measurement of angular momentum(Js)

#Result
print "uncertainity in measurement of angular momentum is",round(deltaL*10**29,2),"*10**-29 Js"

uncertainity in measurement of angular momentum is 2.17 *10**-29 Js

Example number 6, Page number 181

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
m=25*10**-3;         #mass(kg)
v=400;               #speed(m/s)
deltap=(2/100)*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**34,2),"*10**-34 m"

uncertainity in position is 5.27 *10**-34 m

Example number 7, Page number 181

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltax=2*10**-10;    #uncertainity in position(m)
m=9.1*10**-31;       #mass(kg)
e=1.6*10**-19;       #charge(coulomb)
V=1000;              #voltage(V)

#Calculations
deltap=h/(2*math.pi*deltax);      #uncertainity in momentum(kg m/s)
p=math.sqrt(2*m*e*V);             #momentum(kg m/s)
pp=deltap*100/p;                  #percentage of uncertainity in momentum

#Result
print "percentage of uncertainity in momentum is",round(pp,1),"%"

percentage of uncertainity in momentum is 3.1 %

Example number 8, Page number 182

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltax=20*10**-10;   #uncertainity in position(m)
me=9.1*10**-31;      #mass of electron(kg)
mp=1.67*10**-27;     #mass of proton(kg)

#Calculations
deltave=h/(2*math.pi*deltax*me);      #uncertainity in velocity of electron(ms-1)
deltavp=h/(2*math.pi*deltax*mp);      #uncertainity in velocity of proton(ms-1)

#Result
print "uncertainity in velocity of electron is",round(deltave*10**-4,2),"*10**4 ms-1"
print "uncertainity in velocity of proton is",round(deltavp,3),"ms-1"
print "answer for uncertainity in velocity of proton given in the book varies due to rounding off errors"

uncertainity in velocity of electron is 5.79 *10**4 ms-1
uncertainity in velocity of proton is 31.545 ms-1
answer for uncertainity in velocity of proton given in the book varies due to rounding off errors

Example number 9, Page number 182

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

#Variable declaration  
h=6.62*10**-34;      #plancks constant(J s)
deltax=8*10**-15;    #uncertainity in position(m)
mp=1.67*10**-27;     #mass(kg)
e=1.6*10**-19;       #charge(coulomb)

#Calculations
deltap=h/(2*math.pi*deltax);      #minimum uncertainity in momentum(kg m/s)
ke=deltap**2/(2*mp*e);            #minimum kinetic energy of proton(eV)

#Result
print "minimum uncertainity in momentum is",round(deltap*10**20,1),"*10**-20 kg m/s"
print "minimum kinetic energy of proton is",round(ke/10**6,2),"MeV"

minimum uncertainity in momentum is 1.3 *10**-20 kg m/s
minimum kinetic energy of proton is 0.32 MeV