Explain why the location of electrons in atoms is uncertain using the Heisenburg uncertainty principle and wave particle duality? Please explain.Part two of this question is that how is the...

Explain why the location of electrons in atoms is uncertain using the Heisenburg uncertainty principle and wave particle duality? Please explain.

Part two of this question is that how is the location of electrons in atoms defined?

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llltkl | College Teacher | (Level 3) Valedictorian

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Wave particle duality for particle such as an electron means that the particle cannot be precisely localized. Instead, it must be thought of as a wave and the wavelength is given by λ= h/p. For a macroscopic object the associated wavelength is trivial. But for a subatomic particle, like an electron, it assumes a very much significant value. The problem, a general one for the particles of low mass, is treated mathematically by Heisenberg in his famous uncertainty principle which  states that uncertainty in position times uncertainty in momentum is of the order of the Planck’s constant, h. i.e. ∆x. ∆p = h. In other words, more precisely we try to specify momentum or position, the more uncertain we are of the other. For a macroscopic object, say a tennis ball of mass 200g, moving at a speed of 100m/s, uncertainty in position works out to be of the order of 10˄-33 which is absolutely negligible on the particle’s scale. But for an electron of mass 10˄-28g, moving at a speed of 10˄8cm/s such uncertainty works out to be of the order of 10˄-8cm, which is quite significant in the subatomic scale. Hence the uncertainty in the location of electrons inside atoms. As for how the location of electrons in atoms defined, there are several representations. Taking an 1s electron as example, the orbital is depicted by shading. Expectedly, the intensity of shading is greatest at the nucleus revealing the position of greatest probability is at the nucleus. As the distance from the nucleus increases, the intensity decreases though it never attains zero intensity. Thus the orbital is defined as specific electronic probability distribution in space.

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