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Uncertainty principle (W. Heisenberg; 1927):
A principle, central to quantum mechanics, that states two complementary parameters (such as position & momentum, energy & time, or angular momentum & displacement) cannot both be known to infinite accuracy; the more you know regarding one, the less you know regarding the other.
It can be reveled in a quite clear way as it associate to position vs. momentum: To see something (let's say an electron), we ought to fire photons at it; they bounce off and come back to us, thus we can "see" it. If you select low-frequency photons, along a low energy, they do not pass on much momentum to the electron; however they give you a very fuzzy picture, thus you have a higher uncertainty in situation so that you can contain a higher certainty in momentum. Conversely, if you were to fire extremely high-energy photons (x-rays or gammas) at the electron, they would provide you a very apparent picture of where the electron is (higher certainty in position), however would impart great deal of momentum to the electron (higher uncertainty in momentum).
In a more general sense, the uncertainty principle tells us that the action of observing changes the observed in fundamental way.
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Using Gauss divergence theorem show that the volume of a sphere of radius 'r' is 4⁄3 πr 3 .
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