Question

(a) Which will have the lower energy, a 4 s or a $4p$ electron in an As atom? (b) How can we use the concept of effective nuclear charge to explain your answer to part (a)?

Short answer

The 4s electron will have lower energy in an As atom because, for a given principal quantum number, the energy of electrons increases as follows: s < p. The concept of effective nuclear charge explains that the 4s electron experiences a higher Z_eff due to its proximity to the nucleus and is more strongly attracted to it, and therefore has a lower energy compared to the 4p electron.

Step-by-step solution

Electronic configuration of arsenic

To answer the question, let's first describe the electronic configuration of arsenic (As) atom. The atomic number of As is 33, meaning that it has 33 electrons. Applying Aufbau's principle, the electron configuration can be represented as: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³

Comparing the energy levels of 4s and 4p electrons

From the electron configuration of As, we see that 4s and 4p are the outermost orbitals and are both partially filled. Generally, the energy of an electron in an orbital is determined by its principal quantum number (n) and the orbital's shape. For a given principal quantum number, the energy of electrons increases as follows: s < p < d < f. In this case, both the 4s and 4p orbitals have the same principal quantum number (n=4), but the shape of the orbitals differs. Since a 4s electron has a lower energy than a 4p electron, we can conclude that the 4s electron in As will have lower energy. So, the answer to part (a) is: 4s electron will have lower energy.

Using the concept of effective nuclear charge to explain the energy difference

The effective nuclear charge (Z_eff) represents the net positive charge experienced by an electron in an atom after considering the repulsion caused by other electrons in the atom. Electrons closer to the nucleus and in inner shells shield the outer electrons from the full nuclear charge. For a given principal quantum number (n), s electrons are generally closer to the nucleus, experiencing a higher Z_eff, and thus are more strongly attracted to the nucleus. This results in lower energy levels for s electrons in comparison to p electrons. In the case of the 4s and 4p electrons in As, the 4s electrons are closer to the nucleus and experience a higher Z_eff, making them more strongly attracted to the nucleus. Due to this, 4s electrons have lower energy than 4p electrons in an As atom. So, the answer to part (b) is: The concept of effective nuclear charge explains that the 4s electron experiences a higher Z_eff due to its proximity to the nucleus, and therefore has a lower energy compared to the 4p electron.

Key concepts

Electron Configuration

Understanding electron configuration is essential for predicting an atom’s chemical properties and behavior. The electron configuration of an atom describes the distribution of its electrons among the various atomic orbitals based on specified rules.

For instance, arsenic (As) with atomic number 33 has the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³. This sequence follows the Aufbau principle, which dictates that electrons fill the lowest energy orbitals first. The Pauli exclusion principle and Hund’s rule are also taken into account, ensuring that electrons occupy their own orbital when possible and that each subshell is half-filled before pairing begins.

The unique arrangement in arsenic features electrons populating up to the 4p subshell, which is important when assessing the atom's orbital energy levels and the influence of effective nuclear charge on these electrons.

Quantum Numbers

Quantum numbers are like the address of electrons, identifying their exact location in an atom. Each electron in an atom is described by a set of four quantum numbers: the principal quantum number (), the angular momentum quantum number (), the magnetic quantum number (), and the spin quantum number ().

The principal quantum number () indicates the main energy level or shell of an electron and is closely tied to its energy. Higher values of correspond to electrons being farther from the nucleus and generally having more energy. For arsenic (As), electrons in both the 4s and 4p orbitals have the same principal quantum number, n=4, placing them in the fourth shell.

Angular momentum quantum number (l) defines the shape of the orbital, with values ranging from 0 (s) to 3 (f). In arsenic, the 4s orbital has an l value of 0, while the 4p orbital has an l value of 1. This difference influences the electron's energy and its distribution within the atom.

Orbital Energy Levels

Orbital energy levels are critical for understanding the structure of an atom and how electrons behave within it. Electrons in lower energy orbitals are generally closer to the nucleus and more tightly bound, making them harder to remove. The energy level of an electron in an orbital is primarily determined by the principal quantum number () but also depends on the subshell as indicated by the angular momentum quantum number ().

In arsenic (As), the 4s and 4p electrons share the same principal quantum number, but different subshells (s and p, respectively). Typically, s orbitals have lower energy than p orbitals, which is why a 4s electron would have lower energy than a 4p electron in the same atom. Considering the concept of effective nuclear charge, the 4s electron experiences a greater attractive force from the nucleus, as it is shielded less by other electrons. This greater effective nuclear charge results in 4s electrons having lower energy compared to 4p electrons, a key factor in predicting the chemical properties and reactions of atoms like arsenic.