Question

What is meant by an orbital?

Short answer

An orbital is a mathematical function that describes the wave-like behavior of an electron or a pair of electrons in an atom, representing the most probable regions where they can be found. Orbitals have various shapes depending on the energy level and angular momentum quantum numbers (l), such as s, p, d, and f orbitals. The energy level of an orbital is determined by the principal quantum number (n) and the angular momentum quantum number (l), with higher values indicating higher energy levels.

Step-by-step solution

Understanding the Wave-like Properties of Electrons

Electrons possess both particle-like and wave-like properties. The wave-like nature of electrons helps us understand how they behave around the nucleus of an atom. Usage of quantum mechanics allows the determination of probability distributions describing the regions where the electron is most likely to be found.

Orbital Shapes

Orbitals come in various shapes that reflect the probability distribution of finding an electron around the nucleus. The shape of an orbital is determined by the energy level and angular momentum quantum numbers (l). 1. s orbitals: Spherical shape and have no directional preference. They have an angular momentum quantum number, l = 0. 2. p orbitals: Dumbbell-shaped and have directional preference. They have an angular momentum quantum number, l = 1. 3. d orbitals: Have more complex shapes with four of them having a cloverleaf shape, whereas one of them is shaped like a dumbbell with a torus around it. They have an angular momentum quantum number, l = 2. 4. f orbitals: Have more complex shapes and have an angular momentum quantum number, l = 3. As we go on to higher orbitals (g, h, etc.), the shapes become more complicated, and their description becomes less intuitive.

Orbital Energy Levels

The energy level of an orbital is determined by two quantum numbers: the principal quantum number (n) and the angular momentum quantum number (l). The higher the value of n, the higher is the energy of the orbital; the higher the value of l, the higher is the energy within a given n. For a hydrogen atom, the relationship between the energy level and these quantum numbers is: E = -13.6 eV / n^2 Where E is the energy of the orbital, eV stands for electron volts (a unit of energy), and n is the principal quantum number (positive integer values like 1, 2, 3, etc.). In summary, an orbital is a region where an electron is most likely to be found in an atom, depending on its energy and angular momentum. The shapes of orbitals give insights into the probability distribution of the electron in an atom, which aids in understanding its behavior and chemical properties.