Heisenberg’s Uncertainty Principle:-
This Principle was based on the
fundamentals of dual nature of matter.
this Principle state that “Its is
impossible to measure simultaneously the position and momentum (and hence,
velocity) of a small microscopic moving substance with absolute accuracy or
certainty”.
So, the mathematical expression for
the Heisenberg’s Uncertainty Principle
simply written as:
∆x ×
∆p
≥ h/4π
Or, ∆x×
m∆v
≥ h/4π
Or, ∆x∆v
≥ h/4πm
Note; That if m is large enough, the uncertainties
∆x and ∆v can be quit small and satisfy the
uncertainty principle.
Explain of Heisenberg’s Uncertainty Principle:-
Werner Heisenberg
a German physicist, determined that
our observation have an effect on the behavior of quantum. Heisenberg’s
uncertainty principle sound difficult to understand. Even the name is kids of
intimidating, but it’s actually easy to comprehend.
Imagine that somebody is blind and
overtime he has developed a technique for determining how far away an object is
by throwing a heavy ball at it. If one throw the heavy ball at a nearly object,
the ball will return quickly, and it’s is known that it’s close. If one throws
the ball at something far off, it’ll take longer to return, and it become
easier to determine that object is far away. The problem that what one throws a
boll---
Especially a heavy one-------- at
some object, the ball will knock the object across the room and may even have
enough momentum to bounce back. One can say where the object was, but not where
it is now. What’s more, one could calculation the velocity of the object after
hit with the ball, But you have no idea what its velocity was before you hit
it.
Moving on the actual thing, it’s is
being presumed that one attempts to measure both the position and momentum of
an electron. To pinpoint the position of the electron one has to use light so
that that the photon of light strikes the electron. As the result of the
hitting, the position as well as the velocity of the electron are disturbed but
the accuracy with which the position of the particle can be measured depends
upon the wavelength of the light used. The uncertainty in the measurement of position
using light of wavelength λ is ±λ.
Therefore, Shorter the wavelength,
the greater is the accuracy. But shorter wavelength means higher frequency and
hence higher energy. This high energy photon on striking the electron changes
its speed as well as direction.
Example: The
uncertainties in the position and velocity of a particle are 10-10 m
and 5.27×10-24 ms-1 respectively.
Calculate the mass of particle, (h= 6.625×10-34 J.s).
Solution:- We have, ∆ x(m∆v)= h/4π
Or, m= h/4π×1/∆ x . ∆v
= 6.625×10-34(kg.m2s-1)/4×3.14×(10-10m)( 5.27×10-24
ms-1 )
= 0.1o kg. ---
No comments:
Post a Comment