Chapter 2 - Electrons in Atoms
What is this thing called the electron?
An Introduction to Quantum Mechanics
In 1926 both Schrödinger and Heisenberg independently formulated a general quantum theory - a new kind of mechanics - capable of dealing with the wave-particle duality of matter. They used quite different mathematical formalisms but both represent different forms of what is now known as quantum mechanics. Schrödinger's mathematics (wave mechanics) involves differential equations and is more familiar to chemists; it is usual to use his equations as the basis of chemical applications of quantum mechanics - quantum chemistry.
When do we use Quantum Mechanics?
Read Engel and Reid
Chapter 13.1
This section attempts to give a more quantitative answer to the question ‘when do we use quantum mechanics?’ than, ‘when we’re talking about really small things’. Crucial to answering this question is the Boltzmann distribution, which you may possibly remember from first year. It is important that you learn this important classical expression for the partitioning of particles (or oscillators, or any collection of systems) between two energy states separated by an energy difference ΔE:
| ni | = | gi |
| |||||
| nj | gj |
(13.2)
where ni is the numbers of atoms that have energy &epsiloni and nj is the number of atoms that have energy εj, gi and gj are the degeneracies of the energy levels- the number of possible ways of arranging the system to get to that energy. k is Boltzmann’s constant (8.314 JK–1 / Avogadro’s Number) and T is the temperature.
