The wave functions for the 1s and 2s orbitals are as follows: 1s c = (1>p)1>2 (1/a3>2 0 ) exp (-r>a0), 2s c = (1>32p)1>2 (1/a3>2 0 ) (2-r>a0) exp(-r>a0) where a0 is a constant (a0 = 53 pm) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the differences in the plots and identify the node in the 2s wave function.

Quantum chemistry is the branch of chemistry centered on the application of quantum mechanics to chemical systems. It provides an understanding of the electronic structure of atoms and molecules, predicting chemical bonding, reaction dynamics, and physical properties of materials.

Specifically, when describing electrons in atoms, quantum chemistry employs wave functions, a concept rooted in the Schrödinger equation. The wave function for an electron in an atom represents a set of mathematical solutions that describe the probability of finding the electron in a particular region around the nucleus. This probability-based approach is what allows quantum chemists to understand and predict the behavior of atoms in various chemical environments.

Atomic orbitals are mathematical functions that describe the regions in space where there is a high probability of finding an electron in an atom. Each orbital is associated with a particular energy level and shape, which are derived from wave functions that satisfy certain quantum mechanical equations.

For example, the 1s orbital, being the simplest, is spherical and represents the lowest energy state in which an electron can exist around a nucleus. In contrast, the 2s orbital is also spherical but includes a region, called a node, where the probability density of finding an electron is zero. These orbital shapes are fundamental to understanding and predicting the chemical bonding and properties of atoms.

Probability density in quantum chemistry refers to how likely it is to find an electron at a particular point in space around the nucleus of an atom. This likelihood is determined by the square of the wave function's amplitude at that point.

The concept is crucial when interpreting wave functions, because it transforms abstract mathematical expressions into tangible information about electron distribution. The probability density is visually represented through plots of wave functions, with regions of higher density indicating where electrons are more likely to be found. Nodes in these plots represent points of zero probability density, crucial for understanding electron configurations and chemical bonding.

Wave function normalization is the process of adjusting the wave function so that the integral of its probability density over all space equals one. This mathematical requirement ensures that the electron represented by the wave function has a 100% probability of being found somewhere in space.

Normalization is not just a formality; it guarantees that quantum mechanical predictions are physically meaningful. For hydrogen atom wave functions like the 1s and 2s orbitals, proper normalization is critical for accurate representation of the electron's behavior and probability density. Understanding and applying normalization is a fundamental skill in quantum chemistry and is essential for analyzing atomic and molecular systems.