Heisenberg's Uncertainty Principle PAGE

Werner Heisenberg's Uncertainty Principle

The Uncertainty Principle

In 1927, Werner Heisenberg introduced the indeterminacy principle, or more commonly known as the uncertainty principle. It appeared in a paper showing how to interpret matrix mechanics in terms of the more familiar concepts of classical physics.Heisenberg proved that if x is the position coordinate of an electron (in a specific state), and p is the momentum of that electron, and that each have been independently measured for many electrons (in the specific state), then: {delta}x {delta}p >= h/2where {delta}x is the precision of x, and {delta} p is the precision of the momentum coordinates, and h is Plank's constant (6.626176* 10 (sup -27)erg-second). Quantum Interdependancy In layman terms, this means that it is physically impossible to measure both the exact position and the exact momentum of a particle at the same time. The more precisely one of the quantities is measured, the less precisely the other is known. Because of the small value of h in everyday units, this principle is only significant on the atomic scale. It is important to note that the uncertainties of {delta} x and {delta} p arise from the quantum structure of matter, and are not due to imperfections in the measurement instruments. One experiment introduced by Heisenberg, which helps clarify this idea, is discussed by Serway (p.1225) with the following illustration. To see an electron, and thus determine it's position, you might use a powerful light microscope. For the electron to be visible, at least one photon of light must bounce off of it, and then pass through the microscope into your eye. A problem occurs here, as the photon transfers some unknown amount of its momentum to the electron. Thus, in the process of finding an accurately position of the electron (by making {delta} x really small), the same light that allows you to see it changes the electron's momentum to an undeterminable extent (makes {delta}p very large).

Why the Uncertainty Principle is Good.

Heisenberg's uncertainty principle proved that Bohr's model of the atom is incorrect. Bohr's model of the hydrogen atom assumes that the electron in the ground state moves in a circular orbit of radius ( r) 0.529*10^-10 m, and the speed of the electron in this state is 2.2*10^6 m/s. Given the exact radius, the uncertainty {delta}r in this model is zero. According to the uncertainty principle, the product, {delta} p{delta}r >= h/2, where {delta}p is the uncertainty in the momentum of the electron in the radial direction. Because the momentum of the electron is mv, we can assume that the uncertainty in its momentum is less that this value. That is, {delta}p < mv = (9.11*10^(-31)kg)*(2.2*10^(6) m/s) = 2.0 *10 ^(-24) kg*m/sFrom the uncertainty principle, the estimated minimum uncertainty in the radial position would be: = h/ (2{delta}p) = 0.26*10^(-10)mThe uncertainty in position is so close to the size of the Bohr radius, thus proving that the Bohr model is incorrect.

Bibliography
    Heelan, Patrick A. (1965). Quantum Mechanics & Objectivity. The Hauge: Martinus Nijhoff.

    "Heisenberg, Werner". (1995). Encyclopedia Britanica, Online.

    "Heisenberg, Werner." (1994). Compton's Interactive Encyclopedia, (CD-ROM). Compton's New Media.

    Serway, Raymond A. (1996). Physics for Scientists & Engineers. (vol. 2). (pp. 1204-1227). San Francisco: Saunders College Publishing.

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