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An atom comprises protons and neutrons, which are contained inside the dense, centralcore called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers: n, l, ml, and ms.

#### Quantum mechanical model

An atom consists of a small, positively charged nucleus surrounded by electrons. The nucleus contains protons and neutrons. Protons have a charge of +1 and a mass of 1.0073 amu. Neutrons have zero charge and a mass of 1.0087 amu. Electrons have a charge of −1 and a mass of 0.00055 amu. The number of protons in the nucleus is called the atomic number (Z) and defines an atom’s elemental identity. The sum of the numbers of protons and neutrons in the nucleus is called the mass number and, expressed in amu, is approximately equal to the mass of the atom. An atom is neutral when it contains equal numbers of electrons and protons.

Various models were proposed to describe the atomic structure explaining the distribution of electrons around the nucleus. The de Broglie relation quantified that electrons have properties of both a particle and a wave. Quantifying this wave–particle duality further, Heisenberg gave the uncertainty principle: the position (associated with the particle nature) and the velocity or the energy (associated with the wave nature) of the electron cannot be determined simultaneously with full precision. The quantum mechanical model gives a more accurate picture of the atomic structure. It describes the three-dimensional position of an electron with a specific energy, contained in an atom, in a probabilistic manner in terms of the square of the wavefunction, ψ2. Atomic wavefunctions, or atomic orbitals, describe the regions in an atom where electrons are most likely to be found.

An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, groups orbitals in terms of location of energy level, or ‘shell’. The angular momentum or azimuthal quantum number, l, groups the orbitals based on their shapes into ‘subshells’. It has integer values from 0 to n – 1 and is represented by letters: s (l = 0), p (l = 1), d (l = 2), f (l = 3), g (l = 4), and h (l = 5). The magnetic quantum number, ml, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. In addition, each electron has a spin quantum number, ms, that can be equal to ±1/2. No two electrons in the same atom can have the same set of values for all four quantum numbers.

This text is adapted fromOpenstax, Chemistry 2e, Section 6.

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