Heisenberg Uncertainty Relation

We know that according to de-Broglie relationship a microscopic particle such as an electron has both wave and particle characters. Heisenberg a German physicist pointed out that we can never measure simultaneously the exact position and the momentum of the microscopic particles which are small as electrons,.this is known as the Heisenberg’s uncertainty principle.
i.e.

” It is not possible to measure simultaneously the position and the momentum of a microscopic particle with absolute accuracy or certainty”.

In simple form we can also say that…
The product of uncertainty in position and uncertainty in momentum of a microscopic particle is always constant and is equal to or greater than h/4π..you can see below :

where,  Δx = uncertainty in measuring exact position
Δp or mΔv uncertainty in measuring exact position

From the above relationship it is evident that:
i) IF Δx is very small : then the position of the microscopic particle can be measured accurately but Δp will be very large which means that momentum or velocity of the particle cannot be measured with accuracy.

ii)  IF Δp is very small : Then the momentum. or velocity of the microscopic particle can be measured accurately but uncertainty will be introduced in measuring its position.

iii) IF Δx is zero : Then the position can be located with absolute accuracy but in this case Δp will be infinity which means that the momentum or velocity of the microscopic particle cannot be measured at all.
It us shown below mathematically :

This is about Heisenberg Uncertainty Principle. In my next posts I’ll discuss more such topics. If you like my post then Subscribe to our newsletter so that you can get daily tutorials.

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2 thoughts on “Heisenberg Uncertainty Relation”

1. Nice post!
A little question comes to my mind about applications of Heisenberg uncertainty principle.What may be the applications of this principle??

2. Thanks for asking the question…

THERE are different application of this uncertainty principle some important application are…
1) The non-existence of the electron in the nucleus.
2)The existence of the neutron,proton & the alpha particle..