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INTRODUCTION
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| In
classical physics it is generally assumed that position and momentum of
a moving object can be simultaneously measured exactly i.e. no uncertainties
are involved in its description. But in microscopic world it is not possible.
It is found that however refined our instruments there is a fundamental
limitation to the accuracy with which the position and velocity of microscopic
particle can be known simultaneously. This limitation was expressed by a
German physicist Werner Heisenberg
in 1927 and known as 'Heisenberg's uncertainty principle'. In microscopic particles we can observe two type of uncertainties viz. 
Uncertainty in position and momentum
Uncertainty in energy and time |
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STATEMENT
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Uncertainty in position and momentum According to Heisenberg's uncertainty principle: |
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It
is impossible to determine both position and momentum of an electron simultaneously.
If one quantity is known then the determination of the other quantity will become impossible. |
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MATHEMATICAL
REPRESENTATION
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| Let Dx = uncertainty in position DP = uncertainty in momentum |
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| According to Heisenberg's uncertainty principle: | ||||
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The
product of the uncertainty in position and the uncertainty in momentum
is in
the order of an amount involving h, which is Planck’s constant. |
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DP
x Dx
³
h/2p -------(i)
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EXPLANATION
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| It
is not difficult to understand the phenomenon of uncertainty. Consider an
example in which we are going to see the position of an electron. We measure
the position an electron is measured with light and observing the light
that it reflects. The light disturbs its momentum. Heisenberg considered an electron that has a definite, known momentum and that passes under a powerful microscope. He realized that measuring the position of an elementary particle alters its momentum in a random manner. |
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| This technique allows the position to be specified with an accuracy comparable to the wavelength of light used in the experiment. However, when the photons are scattered from the electron, they alter its momentum, because the photons have a momentum of their own. The observer cannot calculate the extent of this disturbance, which is random. | ||||
| Increasing the wavelength decreases the disturbance, because photons of longer wavelength have less momentum and energy. However, increasing the wavelength reduces the precision of the measurement of position. Decreasing the wavelength allows better position measurement, but increases the disturbance to the momentum. | ||||
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UNCERTAINTY
IN
TIME AND ENERGY |
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| Similar
to uncertainty in position there is another principle of uncertainty which
limits the accuracy in the measurement of time i.e. if DE
is the energy uncertainty in time Dt then
we have an expression similar to equation (i) i.e. |
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DE
x Dt
³
h/2p -------(ii)
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RESULTS
OF
UNCERTAINTY PRINCIPLE |
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It is impossible to chase an electron around the nucleus.
The principle describes the incompleteness of Bohr's atomic theory.
According to Heisenberg's uncertainty principle there is no circular orbit
around the nucleus.
Exact position of an electron can not be determined precisely. |
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LIMITATIONS
OF PRINCIPLE
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| Heisenberg's uncertainty principle is not applicable in our daily life. It is only applicable on micro objects i.e. subatomic particles. | ||||
| The reason why the uncertainty principle is of no importance in our daily life is that Planck's constant 'h' is so small (6.625 x 10-34 joule-seconds) that the uncertainties in position and momentum of even quiet small (not microscopic objects) objects are far too small to be experimentally observed. For microscopic phenomena such as atomic processes, the displacements and momentum are such that the uncertainty relation is critically applicable. | ||||
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us:
info@citycollegiate.com |
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