Write the electron configuration of germanium whose atomic number is 32.

The atomic number is a fundamental characteristic of an element, symbolized as 'Z'. It represents the number of protons found in the nucleus of an atom and defines the element's placement in the periodic table. Since protons and electrons are equal in number in an electrically neutral atom, the atomic number also indicates the number of electrons in the atom.

For instance, germanium has an atomic number of 32, which means it contains 32 protons and, correspondingly, 32 electrons. Understanding the atomic number is pivotal because it guides the electron configuration process, helping us to fill the correct number of electrons into the atomic orbitals.

Quantum numbers are the values that describe the unique quantum state of an electron in an atom. There are four quantum numbers—principal (n), azimuthal (l), magnetic (m_l), and spin (m_s). The

• Principal quantum number (n) indicates the shell level and energy of the electron and can be any positive integer.
• Azimuthal quantum number (l) defines the subshell (type of orbital, such as 's', 'p', 'd', or 'f') and can range from 0 to n-1.
• Magnetic quantum number (m_l) describes the orientation of the orbital in space and can range from -l to +l.
• Spin quantum number (m_s) represents the direction of the electron's spin and can be either +1/2 or -1/2.

These quantum numbers not only dictate the placement of electrons within the orbitals but also the energy level, shape, and orientation of these orbitals within an atom. They are essential for determining the electron configuration and for the understanding of the electronic structure of an element.

Pauli's Exclusion Principle is a quantum mechanical principle which states that no two electrons in an atom can have the same set of four quantum numbers. This means that each electron must occupy its unique quantum state.

Due to this principle, atomic orbitals can hold a maximum number of electrons with opposite spins. Specifically, 's' orbitals can hold 2 electrons, 'p' orbitals 6, 'd' orbitals 10, and 'f' orbitals 14. Applying this rule is critical when distributing the electrons among available orbitals to determine an atom's electron configuration.

For example, when writing the electron configuration for germanium, we place the electrons into the orbitals following the increasing energy levels while making sure that no orbital violates Pauli's Exclusion Principle, resulting in the correct configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p².