State Heisenberg Uncertainty Principle
State Heisenberg Uncertainty Principle :- According to Heisenberg it is impossible to measure the position and momentum of a particle simultaneously with 100% accuracy. This is called Heisenberg Uncertainty Principle.
If Δx and Δp are the uncertainties in determining the position and momentum of the particle simultaneously, then
here h = 6.63 × 10-34Js is Plank’s constant
From equation (1) if we are able to measure the exact position of the particle(Δx = 0) then the uncertainty in the measurement of its linear momentum is infinite(Δp→∞). In the same way if we are able to measure the exact linear momentum of the particle(Δp = 0) then we cannot measure the exact position of the particle at that time.
∴ Δx = 0, then Δp→∞ and if Δp = 0 then Δx→∞
If we have to observe an electron then it cannot be done without light and when light(photons) falls on electron, then it’s momentum changes as shown in figure below :-
Uncertainty Principle is a fundamental part of nature and it holds for all microscopic and macroscopic particles.
Other forms of Heisenberg Uncertainty Principle
(State Heisenberg Uncertainty Principle)
(a) In terms of position and velocity :-
As momentum p = mv, Δp = mΔv, so from equation (1), we get
(b) In terms of energy and time :-
Now by dividing and multiplying equation (1) by Δt, we get
As Δp = FΔt, so
As FΔx = ΔE, hence
(c) In terms of angular momentum and angular displacement :-
If the trajectory of the particle is circular with radius
where Δl is the uncertainty in the measurement of position along the trajectory.
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