Question

Write the expected electron configurations for each of the following atoms: \(\mathrm{Sc}, \mathrm{Fe}, \mathrm{P}, \mathrm{Cs}\), Eu, \(\mathrm{Pt}, \mathrm{Xe}, \mathrm{Br}\).

Short answer

The electron configurations for the given atoms are: 1. Sc: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^1\) 2. Fe: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\) 3. P: \(1s^2 2s^2 2p^6 3s^2 3p^3\) 4. Cs: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1\) 5. Eu: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^7\) 6. Pt: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^9\) 7. Xe: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6\) 8. Br: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^5\)

Step-by-step solution

Identify the atomic number

Using a periodic table, find the atomic number (the number of protons) for each of the given elements. These are the atomic numbers of each element: Sc(21), Fe(26), P(15), Cs(55), Eu(63), Pt(78), Xe(54), Br(35).

Order of electron filling

Electron filling follows the aufbau principle, which means that electrons fill the orbitals of lowest energy first. The order of electron filling is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

Electron configuration

Using the atomic numbers and the order of electron filling, we can now write the electron configurations for each element: 1. Sc (Scandium, atomic number 21): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^1\) 2. Fe (Iron, atomic number 26): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\) 3. P (Phosphorus, atomic number 15): \(1s^2 2s^2 2p^6 3s^2 3p^3\) 4. Cs (Cesium, atomic number 55): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1\) 5. Eu (Europium, atomic number 63): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^7\) 6. Pt (Platinum, atomic number 78): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^9\) 7. Xe (Xenon, atomic number 54): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6\) 8. Br (Bromine, atomic number 35): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^5\) These are the electron configurations for the given atoms.

Key concepts

Periodic Table

The periodic table is a master chart of all known elements, organized by atomic number, electron configurations, and recurring chemical properties. Elements are listed in order of increasing atomic number, which is the number of protons in an atom's nucleus, and by rows (periods) which correlate to the number of electron shells.

Each column (group) contains elements with similar chemical behaviors due to the similar outer electron configuration. For example, Group 1 elements, also known as alkali metals, all have a single electron in their outermost shell, making them highly reactive. In contrast, Group 18 elements, the noble gases like Xenon (Xe), have full outer shells, which accounts for their lack of reactivity.

The periodic table also reflects the shell structure of elements’ electron configurations, which determine an element's chemical properties. The table is designed so that elements with similar electron configurations and, thus, similar properties appear in vertical columns, aiding in the prediction of an element's behavior when reacting or combining with other elements.

Aufbau Principle

The aufbau principle is a fundamental concept used to determine the electron configurations of atoms. It states that electrons are added to the lowest energy orbitals first before moving on to higher energy orbitals. This ‘building-up’ basis is the essence of the aufbau principle, which is German for 'building up.'

According to the principle, the orbitals are filled in a specific sequence, which generally follows the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. However, there are some exceptions due to the closeness in energy of certain orbitals like 3d and 4s. This means an electron may enter a 4s orbital before a 3d orbital if it results in a lower total energy for the atom.

Understanding the aufbau principle helps in writing electron configurations, as seen in the exercise. For example, Scandium (Sc) has an atomic number of 21, so the configuration starts at 1s and is built up to 3d, where it has its last electron. The principle, combined with Hund's rule and the Pauli exclusion principle, forms the basis for filling the electron orbitals in an atom.

Atomic Number

The atomic number is a fundamental characteristic of an element, denoting the number of protons in the nucleus of an atom. It determines the element's position on the periodic table and defines its chemical identity. For instance, Carbon will always have an atomic number of 6, meaning any atom with 6 protons is considered Carbon.

The atomic number is not just a position marker on the periodic table; it also tells us the number of electrons in a neutral atom, since the number of electrons equals the number of protons to maintain charge neutrality. The atomic number therefore is crucial in determining the electron configuration of an element. For phosphorus (P) with an atomic number of 15, one can deduce it has 15 electrons, which are arranged in orbitals following the aufbau principle to give the electron configuration presented in the exercise.