Quantum Mechanics 2

# Quantum Mechanics 2 - ISP 209 lecture History of science...

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ISP 209 lecture History of science, 1920 – 1960 Atoms, the nucleus, and subatomic particles Quantum mechanics

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Back to de Broglie Why do electrons stay in certain orbitals? Unlike planets, which can have any radius in orbiting the Sun De Broglie suggested that all particles have a wave nature, with wavelength λ = h/p The wave nature of the electron determines the nature of the orbits An integral number of wavelengths must fit in an orbital
An explanation This model explained why electrons don’t spiral closer and closer to the nucleus. Each electron orbit is described by a standing wave. The circumference of the smallest orbit can be no smaller than one wavelength.

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Quantum mechanics Electron waves move not only around the nucleus, but also in and out, toward and away from the nucleus In the 1920’s physicists such as Wolfgang Pauli, Erwin Schroedinger, Werner Heisenberg and others realized that you cannot talk about a classical concept such as a fixed orbit for a subatomic particle like an electron Instead you can only describe the probability for an electron to be in a particular location at a particular time So we have an “electron cloud” picture of an atom The electrons aren’t pulverized; the cloud is a probability cloud
Quantum mechanics It was the end of certainty Quantum mechanics describes only probabilities given in terms of the square of a wave function ψ (x) The wave function is a solution to an equation called the Schroedinger equation Schroedinger’s equation replaces newton’s equation (a=F/m) The probability wave in Schroedinger’s equation is a mathematical entity, not directly observable | ψ | 2 gives the probability of finding The electron at a given location

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Quantum mechanics One can calculate the probability values for the momentum or position or energy of a particle by solving the Schroedinger equation We can’t talk about the specific location of an electron at a given moment in time --- only the probability that it is at a particular location at a particular moment in time Its most probable location is at the average distance from the nucleus for the orbitals defined by Niels Bohr | ψ | 2 gives the probability of finding The electron at a given location
The advance in understanding The theory advanced from the orbitals described by Niels Bohr, to de Broglie’s standing waves, to a probability cloud describing the electron location, in about 1 decade (1918-1928).

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