# Chapter 4:The Wave Like Properties of Particles¶

## Example 4.1 Page 101¶

In [3]:
#initiation of variable
from math import sqrt
h=6.6*10**-34;                              # h(planck's constant)= 6.6*10^-34
m1= 10.0**3;v1=100.0;                           # for automobile

#calculation
w1= h/(m1*v1);                            # ['w'-wavelength in metre'm'-mass in Kg 'v'-velocity in metres/sec.] of the particles
m2=10.0*(10**-3);v2= 500;                     # for bullet
w2=h/(m2*v2);
m3=(10.0**-9)*(10.0**-3); v3=1.0*10**-2;
w3=h/(m3*v3);
m4=9.1*10**-31;k=1*1.6*10**-19;            # k- kinetic energy of the electron & using 1ev = 1.6*10^-19 joule
p=sqrt(2.0*m4*k);                         # p=momentum of electron ;from K=1/2*m*v^2
w4=h/p;
hc=1240;pc=100                         # In the extreme relativistc realm, K=E=pc; Given pc=100MeV,hc=1240MeV
w5= hc/pc;

#result
print "Wavelength of the automobile in m is",w1;
print "Wavelength of the bullet in m is ",w2 ;
print"Wavelength of the smoke particle in m is",w3 ;
print "Wavelength of the electron(1ev) in nm is",round(w4*10**9,3) ;
print "Wavelength of the electron (100Mev) in fm is",w5;

Wavelength of the automobile in m is 6.6e-39
Wavelength of the bullet in m is  1.32e-34
Wavelength of the smoke particle in m is 6.6e-20
Wavelength of the electron(1ev) in nm is 1.223
Wavelength of the electron (100Mev) in fm is 12


## Example 4.2 Page 113¶

In [4]:
#initiation of variable
from math import pi
# w=wavelength; consider k=2*(pi/w);
# differentiate k w.r.t w and replace del(k)/del(w) = 1 for equation.4.3
# which gives del(w)= w^2 /(2*pi*del(x)), hence
w=20; delx=200; # delx=200cm and w=20cm

#calculation
delw=(w**2)/(delx*2*pi);

#result
print "Hence uncertainity in length in cm is",round(delw,3);

Hence uncertainity in length is in cm 0.318


## Example 4.3 Page 114¶

In [6]:
#initiation of variable
from math import pi
delt=1.0;             #consider time interval of 1 sec
delw=1/delt;        # since delw*delt =1 from equation 4.4
delf=0.01          #calculated accuracy is 0.01Hz

#calculation
delwc =2*pi*delf # delwc-claimed accuracy from w=2*pi*f

#result
print "The minimum uncertainity calculated is 1rad/sec. The claimed accuracy in rad/sec is \n",round(delwc,3);
print "thus there is a reason to doubt the claim"

The minimum uncertainity calculated is 1rad/sec. The claimed accuracy is in rad/sec
0.063
thus there is a reason to doubt the claim


## Example 4.4 Page 115¶

In [4]:
#initiation of variable
from math import pi
m=9.11*10**-31;v=3.6*10**6; #'m','v' - mass an velocity of the electron in SI units
h=1.05*10**-34; #planck's constant in SI
p=m*v; #momentum
delp=p*0.01; #due to 1% precision in p
delx = h/delp; #uncertainity in position

#result
print "Uncertainty in position in nm is",round(delx*10**9,2);

#partb
print "Since the motion is strictly along X-direction, its velocity in Y direction is absolutely zero.\n So uncertainity in velocity along y is zero=> uncertainity in position along y is infinite. \nSo nothing can be said about its position/motion along "

Uncertainity in position in nm is 3.2
Since the motion is strictly along X-direction, its velocity in Y direction is absolutely zero.
So uncertainity in velocity along y is zero=> uncertainity in position along y is infinite.
So nothing can be said about its position/motion along


## Example 4.5 Page 116¶

In [5]:
#initiation of variable
from math import pi
m=0.145;v=42.5; #'m','v' - mass an velocity of the electron in SI units
h=1.05*10**-34; #planck's constant in SI
p=m*v; #momentum
delp=p*0.01;#due to 1% precision in p

#calculation
delx = h/delp#uncertainty in position

#result
print "Uncertainity in position is %.1e" %delx;

#part b
print "Motion along y is unpredictable as long as the velocity along y is exactly known(as zero).";

Uncertainity in position is 1.7e-33
Motion along y is unpredictable as long as the veloity along y is exactly known(as zero).


## Example 4.7 Page 119¶

In [14]:
#initiation of variable
from math import sqrt
mc2=2.15*10**-4;          #mc2 is the mass of the electron, concidered in Mev for the simplicity in calculations
hc=197.0                  # The value of h*c in Mev.fm for simplicity
delx= 10.0               # Given uncertainty in position=diameter of nucleus= 10 fm

#calculation
delp= hc/delx ;       #Uncertainty in momentum per unit 'c' i.e (Mev/c) delp= h/delx =(h*c)/(c*delx);hc=197 Mev.fm  1Mev=1.6*10^-13 Joules')
p=delp;               # Equating delp to p  as a consequence of equation 4.10
K1=p**2+mc2**2   # The following 3 steps are the steps invlolved in calculating K.E= sqrt((p*c)^2 + (mc^2)^2)- m*c^2
K1=sqrt(K1)
K1= K1-(mc2);

#result
print "Kinetic energy was found out to be in Mev is", round(K1,3)

Kinetic energy was found out to be in Mev 19.7


## Example 4.8 Page 120¶

In [9]:
#initiation of variable
h=6.58*10**-16; # plack's constant
delt1=26.0*10**-9;E1=140.0*10**6 #given values of lifetime and rest energy of charged pi meson
delt2=8.3*10**-17;E2=135.0*10**6;  #given values of lifetime and rest energy of uncharged pi meson
delt3=4.4*10**-24;E3=765*10**6;       #given values of lifetime and rest energy of rho meson

#calculation
delE1=h/delt1; k1=delE1/E1;  # k is the measure of uncertainity
delE2=h/delt2; k2=delE2/E2;
delE3=h/delt3; k3=delE3/E3;

#result
print "Uncertainty in energy of charged pi meson is %.1e" %k1;
print "Uncertainty in energy of uncharged pi meson is %.1e" %k2;
print "Uncertainty in energy of rho meson is ",round(k3,2);

Uncertainity in energy of charged pi meson is 1.8e-16
Uncertainity in energy of uncharged pi meson is 5.9e-08
Uncertainity in energy of rho meson is  0.2


## Example 4.9 Page 121¶

In [17]:
#initiation of variable
h=1.05*10**-34;  #value of planck's constant in J.sec
delx= 1.0;        # uncertainty in positon= dimension of the ball
delp=h/delx;    # uncertainty in momentum
m=0.1;         #mass of the ball in kg

#calculation
delv=delp/m;    # uncertainty in velocity

#result
print "The value of minimum velocity was found out to be in m/sec",delv;

The value of minimum velocity was found out to be in m/sec 1.05e-33