Question

(a) Which will have the lower energy, a \(4 s\) or a \(4 p\) 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

(a) A 4s electron in an As atom has lower energy than a 4p electron. (b) We use the concept of effective nuclear charge to account for shielding effects of inner electrons, which reduces the attraction between the nucleus and the outer electrons. Comparing the effective nuclear charges for 4s and 4p electrons in an As atom, we find that 4s electrons have a higher effective nuclear charge than 4p electrons, which indicates a stronger attraction to the nucleus, and hence, lower energy.

Step-by-step solution

Identify the electron configurations of Arsenic

First, let's find out the electron configuration of an Arsenic (As) atom. Arsenic has an atomic number of 33, which means it has 33 electrons. The electron configuration can be determined by filling the electrons in the orbitals following the Aufbau principle. The electron configuration of As is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3\]

Define the effective nuclear charge

The effective nuclear charge (\(Z_{eff}\)) represents the net positive charge experienced by an electron in an atom. This net charge takes into account the shielding effect caused by other electrons present in the atom. The shielding effect reduces the electrostatic attraction between the nucleus and the outer electrons. So, the effective nuclear charge can be written as: \[Z_{eff} = Z - S\] Where \(Z\) is the atomic number (total protons in the nucleus), and \(S\) is the shielding constant.

Determine the shielding constant for 4s and 4p electrons

Next, we need to find the shielding constant for both 4s and 4p electrons. For a 4s electron, all the electrons in the lower shells contribute to shielding. So, the shielding constant for a 4s electron is: \(S_{4s} = 1(2) + 2(2) + 2(6) + 3(2) + 3(6) + 3(10)\) Evaluate \(S_{4s}\) to get the shielding constant: \(S_{4s} = 2 + 4 + 12 + 6 + 18 + 30 = 72\) Similarly, for a 4p electron, the shielding constant can be calculated as: \(S_{4p} = 1(2) + 2(2) + 2(6) + 3(2) + 3(6) + 3(10) + 4(2)\) Evaluate \(S_{4p}\) to get the shielding constant: \(S_{4p} = 2 + 4 + 12 + 6 + 18 + 30 + 8 = 80\)

Calculate the effective nuclear charges for 4s and 4p electrons

Now, we can calculate the effective nuclear charges for both 4s and 4p electrons using the shielding constants. For a 4s electron: \(Z_{eff_{4s}} = Z - S_{4s} = 33 - 72 = -39\) For a 4p electron: \(Z_{eff_{4p}} = Z - S_{4p} = 33 - 80 = -47\)

Compare the effective nuclear charges and determine the lower energy orbital

Finally, we can compare the effective nuclear charges to find out which orbital has lower energy. Since the effective nuclear charge of 4s electrons is higher than that of 4p electrons (-39 > -47), the 4s electrons experience a stronger attraction to the nucleus, and hence have lower energy. So, a 4s electron in an As atom has lower energy than a 4p electron. (b) The concept of effective nuclear charge provides an explanation for the different energy levels of 4s and 4p electrons in an As atom. It takes into account the shielding effect caused by other electrons, reducing the electrostatic attraction between the nucleus and the outer electrons. This helps us compare the energies of 4s and 4p electrons, explaining why 4s electrons have lower energy than 4p electrons in an As atom, as seen in the calculations above.

Key concepts

Electron Configuration

Understanding the electron configuration of an atom is crucial for predicting its chemical behavior. Electron configuration refers to the distribution of electrons in an atom's orbitals. Electrons fill orbitals in a particular order, dictated by their energy levels, with lower energy levels filling up first before moving on to the higher ones.

In the case of arsenic (As), with an atomic number of 33, it holds 33 electrons. These electrons are distributed across various shells and subshells: from the 1s orbital up through to the 4p subshell, following the sequence 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³. Each number indicates the principal quantum level (shell), and each letter represents a subshell type (s, p, d, f), with the superscript indicating the number of electrons in that subshell. This arrangement leads us into the next key concept: the Aufbau principle.

Aufbau Principle

The Aufbau principle, a guideline for electron placement, states that electrons fill the lowest energy orbitals first before occupying higher energy levels. 'Aufbau' is German for 'building up', reflecting this method of 'building up' electron configurations by progressively adding electrons to orbitals.

As part of this principle, there's a specific order to how electrons populate orbitals: they start at the lowest energy level, which is the 1s orbital, and work their way up to higher energy levels. The order can be remembered through a specific chart or by following the diagonal rule. In this way, the Aufbau principle helps predict the electronic structure of an atom, which significantly affects its properties and the type of chemical bonds it can form.

However, the rule is not absolute and can be influenced by certain factors such as electron-electron interactions and the overall energy of the atom. This leads to exceptions, especially for atoms with a large number of electrons or those with electrons in d and f subshells.

Shielding Effect

The shielding effect describes how inner-shell electrons can block the attractive force of the nucleus from the valence (outer) electrons. This screening makes the effective nuclear charge felt by outer electrons less than the actual charge of the nucleus.

The shielding effect can affect chemical reactivity and properties such as ionization energy and atomic radius. Electrons in the same energy level have little shielding effect on each other; however, electrons in inner levels provide a larger barrier and lower the effective nuclear charge felt by outer-level electrons.

In arsenic, for example, 4s electrons feel a different effective nuclear charge than 4p electrons due to the shielding from electrons in the inner shells. The effective nuclear charge is calculated by subtracting the shielding constant, which quantifies the extent of shielding, from the atomic number representing the full charge of the nucleus. The outcome of this calculation, as shown in the exercise, helps to understand why 4s electrons are at a lower energy level compared to 4p electrons. The increased nuclear attraction for 4s electrons compared to 4p electrons due to the shielding effect explains their position in the energy level hierarchy.