Atomic Orbital

The various energy shells composed of electron distribution surrounding the nucleus of an atom is known as the atomic orbitals. These orbitals represent the density distribution of electrons that float around the atom, and are filled with new electrons as the atom increases in size. An atomic orbital is a mathematical function that describes the wave- like behavior of either one electron or a pair of electrons in an atom. This function can also be used to calculate the probability of finding any electron of an atom in any specific region around the atom’s nucleus. The term may also be used to refer the physical region by the function where the electron is likely to be.

Within a physical context atomic orbitals are the basic building blocks of the electron cloud model, which is a modern framework for describing the placements of electrons in an atom. Atomic orbitals are typically described as “hydrogen- like” (meaning one electron) wave functions over space, categorized by n, l and m quantum numbers, which correspond to the electron’s energy, angular momentum and an angular momentum direction, respectively.

The simple names s orbital, p orbital, d orbital and f orbital refer to orbitals with angular momentum quantum number l= 0, 1, 2 and 3 respectively. These names are used to indicate the orbital shape and to explain the electron configurations. They are derived from the characteristics of their spectroscopic lines: sharp, principal, diffuse and fundamental, the rest being named in alphabetical order.

Wave- like properties

The electrons of the nucleus exist of standing waves, unlike a planet orbiting a sun. Therefore the lowest possible energy an electron can take is analogous to the fundamental energy of a wave on a string.

Particle- like properties

There are always an integer number of electrons orbiting the nucleus. Electrons jump between orbitals in a particle- like fashion.

Shapes of Orbitals

The shape of the orbitals depends on many factors. The most important are the quantum numbers associated with the particular energy stage. These are n, the principal quantum number, l, the orbital quantum number and m, the angular momentum. The shapes of the atomic orbitals in one- electron atom are related to 3- dimensional spherical harmonics. These shapes are not unique and any linear combination is valid like a transformation to cubic harmonics. Some of the shapes include single s orbital, three p orbital and the seven f orbitals.

Questions:

• What is an Atomic Orbital?
• What are the factors on which the shape of an atomic orbital depends on?