What is the NL rule?

As a domain expert in quantum chemistry, I'm delighted to discuss the NL rule, which is an essential concept in understanding the electronic configurations of atoms. The NL rule, also known as the Madelung's rule or the diagonal rule, is a guideline that helps predict the order in which atomic orbitals are filled with electrons. To begin with, let's establish some fundamental quantum mechanical principles. Electrons in atoms are described by four quantum numbers: 1. Principal Quantum Number (n): This defines the energy level of the electron and determines the size of the orbital. It can take on any positive integer value (n = 1, 2, 3, ...). 2. Angular Momentum Quantum Number (l): This describes the shape of the orbital and is related to the orbital's angular momentum. It can take on integer values from 0 to (n-1), corresponding to different subshells (s, p, d, f, ...). 3. Magnetic Quantum Number (m_l): This determines the orientation of the orbital in space and can take on values from -l to +l, including 0. 4. Spin Quantum Number (m_s): This describes the electron's spin, which can be either +1/2 (spin up) or -1/2 (spin down). The NL rule is particularly concerned with the first two quantum numbers, n and l. According to this rule, when filling the orbitals in an atom, the orbitals are filled in an order that is determined by the sum of these two quantum numbers (n + l). The rule states that orbitals with the lowest sum are filled first. This is crucial for understanding the electron configuration of atoms and the periodic table. Let's delve into the specifics: - s orbitals (l = 0) are filled before p orbitals (l = 1), because s orbitals have a lower sum of quantum numbers (n + l). - p orbitals are filled before d orbitals (l = 2), and so on. The rule also takes into account the energy levels associated with the principal quantum number n. For example, the 2s orbital is filled before the 3p orbitals, even though both have the same sum of quantum numbers (2 + 0 = 1 for 2s and 3 + 1 = 4 for 3p), because the 2s orbital is lower in energy. The NL rule is not without exceptions, and there are a few irregularities in the filling order that can occur due to various factors such as electron-electron repulsion and the stability provided by a half-filled or fully-filled subshell. However, these exceptions are relatively rare, and the rule provides a good general guideline for predicting electron configurations. Now, let's translate this into Chinese.

For equal values, the orbital with the lower is most often filled first. Here is the principal quantum number and is the angular momentum quantum number , designated by the code , , , for , respectively. The " rule," also known as the Madelung rule or the diagonal rule, holds with only a small number of irregularities.