Skip to main content

Easy Notes on Heisenberg uncertainty principle.

 Heisenberg Uncertainty principle

Statement

According to uncertainty principle it is impossible to measure the momentum (i.e velocity) and position of the particle simultaneously with accuracy. 
The product of uncertainties in position and momentum is equal to or greater than Planck's constant or h/2π or h/4π.
∆x.∆p ≥ h .....(1)
A more exact derivation
∆x.∆p≥ h/2π
Where ∆x is the uncertainty in position and ∆p is the uncertainty in momentum.
From eqn(1) it is evident that if we try to measure the position of particle with utmost accuracy i.e ∆x➝ 0, the corresponding uncertainty in momentum becomes very large ∆p➝∞
∆p≥h/∆x
∆p≥h/0
∆p≥∞
and vice versa.

Its extension to Energy and time.

The time energy uncertainty principle states that it is impossible to determine the energy and time of particle simultaneously with a desire accuracy.
Let ∆E be the uncertainty in energy and ∆t be the uncertainty in time then
∆E.∆t  ≥ h
A more exact derivation
∆E.∆t ≥ h/2π
∆E.∆t ≥ h/4π
Derivation of Heisenberg Uncertainty principle.
Derivation of uncertainty principle.
Derivation of uncertainty principle and its extension.
Derivation of uncertainty principle and its extension.


Conclusion

The uncertainty principle is applicable to all objects but its consequences are significant only for minute particle of microscopic size as electrons, protons, neutrons etc, because in case of macroscopic (large size) objects the uncertanties in the measurement of these quantities are so large that their product exceed the value of Planck's constant h by many orders of magnitude. Thus due to the smallness of Planck's constant, the uncertainty principle becomes meaningless for measurements in connection with macroscopic bodies.

Fill in the blanks

1) According to uncertainty principle it is impossible to measure the position and ________ of the particle simultaneously with accuracy.
2) According to uncertainty principle  it is impossible to measure energy and _____ simultaneously.
3) The product of uncertainties in position and momentum is equal to or greater than ______ .
4) ∆x.∆p ≥ ____
5) If we try to measure the position of particle with utmost accuracy, the corresponding uncertainty in momentum becomes very ______.
6)If ∆x➝ ___,  ∆p➝∞.
7) The uncertainty principle is applicable to ____ objects.
8) The consequences of uncertainty principle are significant only for _____ particle.
9) The uncertainty principle becomes meaningless for measurements in connection with ________ bodies.
10) The uncertainty principle is also called ________.
Ans)1) According to uncertainty principle it is impossible to measure the position and momentum of the particle simultaneously with accuracy.
2) According to uncertainty principle  it is impossible to measure energy and time simultaneously.
3) The product of uncertainties in position and momentum is equal to or greater than Planck's constant .
4) ∆x.∆p ≥ h
5) If we try to measure the position of particle with utmost accuracy, the corresponding uncertainty in momentum becomes very large.
6)If ∆x➝ 0,  ∆p➝∞.
7) The uncertainty principle is applicable to all objects.
8) The consequences of uncertainty principle are significant only for minute particle.
9) The uncertainty principle becomes meaningless for measurements in connection with macroscopic bodies.
10) The uncertainty principle is also called Heisenberg Uncertainty principle.

Comments

Post a Comment

Popular posts from this blog

LS coupling and jj coupling.

 Total angular momentum: The total angular momentum of an electron is the sum of the orbital angular momentum and spin angular momentum of the electron i.e Coupling Scheme Since an atom consist of large number of electrons having different orbital and spin momenta, Coupling scheme is necessary to obtain the resultant orbit and spin momenta of atom as a whole. There are two types of coupling scheme namely 1) LS Coupling 2) JJ Coupling. 1)LS Coupling: In this coupling the 'l' vectors of all electrons combine to form resultant 'L' vector and all the 's' vectors of these electrons combine to form resultant 'S' vector. Then the 'L' vector and 'S' vector undergoes vector addition to give resultant 'J' vector which represents the total angular momentum of an atom. Symbolically LS coupling is represented as This type of coupling is governed by the following principles: 1) All the three vectors (L,S and J vectors) are quantized. 2)L is an ...
Post a Comment
Read more

Mass defect, packing fraction and binding energy.

 Mass defect, packing fraction and binding energy: It was assumed that mass of the nucleus is equal to the mass of its constituents (i.e protons and neutrons). But experimentally it was found that the actual mass of the nucleus is less than the theoretical mass. Thus, the difference between the theoretical mass and experimental mass is called mass defect i.e ∆m={[Zmₚ + (A-Z)mₙ] - M} Where mₚ= mass of proton              mₙ= mass of neutron               M= actual mass of nucleus                Z= atomic number                A= mass number The ratio of mass defect and mass number (A) is called packing fraction (f) f = ∆m/A Thus packing fraction is the mass defect available per nucleon. The packing fraction explains the stability of the nucleus. The packing fraction may be positive, negative or zero. The positive value of packing fract...
Post a Comment
Read more

Gamma decay.

 Gamma decay A nucleus can exist in states whose energies are higher than that of its ground state, as an atom can. An excited nucleus is denoted by an asterisk on its usual symbol. The excited nucleus return to its ground state by emitting photon whose energy corresponds to the energy difference between initial and final states in the transition involved. The photons emitted by the nucleus have energy in the range of several MeV and is traditionally called gamma decay. Unlike, alpha decay and beta decay, the parent nucleus does not undergo any physical change in the process, daughter and parent nuclei are the same. Most of the time, gamma decay occurs after the radioactive nuclei have undergone an alpha or a beta decay. The alpha and beta decays leave the daughter nuclei in an excited state. From the excited state, the daughter nuclei can get back to the ground state by emitting one or more high energy gamma rays.  The relationship between decay and energy level is shown in f...
Post a Comment
Read more