Consider the changes in the distribution of nine particles into three interconnected boxes shown here. Which has the most negative \(\Delta S\) ?
Quantum Numbers and Atomic Orbitals By solving the Schrödinger equation (Hψ = Eψ), we obtain a set of mathematical equations, called wave functions (ψ), which describe the probability of finding electrons at certain energy levels within an atom. A wave function for an electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in which there is a high probability of finding the electron. Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy (usually accompanied by the absorption or emission of a photon of light). Each electron in an atom is described by four different quantum numbers. The first three (n, l, m)lspecify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital. 1. Principal Quantum Number (n): n = 1, 2, 3, …, ∞ Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of the peak in a radial probability distribution plot). All orbitals that have the same value of n are said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of orbitals for a given n value is n2. 2. Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n1. Specifies the shape of an orbital with a particular prin