Chapter 18 Uncertainty Principle and Quantum Statistics

Example 18.1 Page no 122

In [9]:
#Given
h=1.05*10**-34
x=10.0**-8
m=9.1*10**-31

#Calculation
p=h/x
v=h/m

#Result
print"Minimum uncertainty in its velocity is",round(v*10**4,2),"*10**4 m/s"

Minimum uncertainty in its velocity is 1.15 *10**4 m/s

Example 18.2 Page no 122

In [21]:
#Given
E=200
m=9*10**-31
e=1.602*10**-19
h=6.626*10**-34
r=10**-6

#Calculation
import math
p=math.sqrt(2*m*E*e)
p1=h/(2*r)
a=p1/p

#Result
print"Uncertainty introduced in the angle of emergence is", round(a*10**5,2),"*10**-6 radians"

Uncertainty introduced in the angle of emergence is 4.36 *10**-6 radians

Example 18.3 Page no 123

In [27]:
#Given
h=1.05*10**-34                     #j-s
v=3*10**7                          #m/s
m0=9*10**-31                       #Kg
c=3*10**8

#Calculation
import math
x=(h/(m0*v))*(math.sqrt(1-(v/c)*2))

#Result
print"Smallest possible uncertainty is", round(x*10**10,3),"A"

Smallest possible uncertainty is 0.039 A

Example 18.4 Page no 123

In [48]:
#Given
h=1.05*10**-34
x=0.0001
m=9*10**-31
X=5*10**-10
m1=1.67*10**-27

#Calculation
p=h/x
v=p*10**-9/(m*X)
M=4*m1
V=p/(M*X)

#Result
print"Uncertainty in the velocity of electron is", round(v,2),"*10**3 m/s"
print"Uncertainty in the velocity of alpha particle is",round(V*10**-4,1),"m/s"

Uncertainty in the velocity of electron is 2.33 *10**3 m/s
Uncertainty in the velocity of alpha particle is 31.4 m/s

Example 18.5 Page no 124

In [56]:
#Given
E=200                   #eV
A=1.6*10**-19           #J
S=9*10**-31
q=2
x=1.05*10**-34          #J.s
y=2*10**-6              #m

#Calculation
import math
P=math.sqrt(q*S*E*A)
P1=x/y
P2=P1/P

#Result
print"The uncertainty introduced in the angle of emergence is",round(P2*10**6,2),"10**-6 radians"

The uncertainty introduced in the angle of emergence is 6.92 10**-6 radians

Example 18.6 Page no 124

In [65]:
#Given
a=1.05*10**4                            #ms**-1
b=0.01 
h=1.05*10**-34                          #Js
m=9*10**-31
s=100

#Calculation
v=h*s/(m*b*h)

#Result
print"The uncertainty in the position of the electron is",round(v*10**-34,1),"10**-4 m"

The uncertainty in the position of the electron is 1.1 10**-4 m

Example 18.7 Page no 124

In [78]:
#Given
q=50                            #g
w=300                           #ms**-1
i=0.01
d=1000.0
e=100.0
h=6.62*10**-34

#Calculation
b=(w*(q/d)*(i/e))
b1=h/(2*math.pi*b)

#Result
print"The accuracy is",round(b1*10**32,0),"10**-32 m"

The accuracy is 7.0 10**-32 m

Example 18.8 Page no 124

In [89]:
#Given
y=10**12
h=6.62*10**-34
a=2

#Calculation
import math
E=h/(a*math.pi*y)
E1=E/h

#Result
print"The probable uncertainty in energy is",round(E*10**46,3),"10**-22 J"
print"The frequency of a gamma-ray is",round(E1*10**13,2),"10**11 Hz"

The probable uncertainty in energy is 1.054 10**-22 J
The frequency of a gamma-ray is 1.59 10**11 Hz

Example 18.9 Page no 125

In [99]:
#Given
h=6.63*10**-34                #J.sec
a=10**-8
b=2

#Calculation
import math
E=h/(b*math.pi*a)
v=E/h

#Result
print"The uncertainty in the energy is",round(E*10**26,3),"10**-26 J"
print"The uncertainty in the frwquency of light is",round(v*10**-7,2),"10**7 Hz"

The uncertainty in the energy is 1.055 10**-26 J
The uncertainty in the frwquency of light is 1.59 10**7 Hz

Example 18.10 Page no 125

In [113]:
#Given
a=10**-8                       #sec
h=1.05*10**-34
l=1.6*10**-19

#Calculation
g=h/a
E=g/l

#Result
print"The limit of accuracy is",round(E*10**8,2)*10**-8,"eV"

The limit of accuracy is 6.56e-08 eV