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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.

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