Question

The elements \(\mathrm{Cu}, \mathrm{O}, \mathrm{La}, \mathrm{Y}, \mathrm{Ba}, \mathrm{Tl},\) and \(\mathrm{Bi}\) are all found in high-temperature ceramic superconductors. Write the expected electron configuration for these atoms.

Short answer

The electron configurations for the given elements are: Cu: \([Ar] 3d^9 4s^2\) O: \([He] 2s^2 2p^4\) La: \([Xe] 4f^1 5d^1 6s^2\) Y: \([Kr] 4d^1 5s^2\) Ba: \([Xe] 6s^2\) Tl: \([Xe] 4f^14 5d^10 6s^2 6p^1\) Bi: \([Xe] 4f^14 5d^10 6s^2 6p^3\)

Step-by-step solution

Find the atomic numbers for each element

Use a periodic table to find the atomic number for each element: Cu (29), O (8), La (57), Y (39), Ba (56), Tl (81), and Bi (83).

Write electron configurations using the Aufbau Principle

Using the Aufbau Principle, fill the orbitals in the same order as they appear in the periodic table. The order of filling is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

Write the electron configurations for each element

Cu (29): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d⁹ \( \Rightarrow \) [Ar] 3d⁹4s² O (8): 1s², 2s², 2p⁴ \( \Rightarrow \) [He] 2s²2p⁴ La (57): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², 4f¹ \( \Rightarrow \) [Xe] 4f¹5d¹6s² Y (39): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹ \( \Rightarrow \) [Kr] 4d¹5s² Ba (56): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s² \( \Rightarrow \) [Xe] 6s² Tl (81): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², 4f¹⁴, 5d¹⁰, 6p¹ \( \Rightarrow \) [Xe] 4f¹⁴5d¹⁰6s²6p¹ Bi (83): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², 4f¹⁴, 5d¹⁰, 6p³ \( \Rightarrow \) [Xe] 4f¹⁴5d¹⁰6s²6p³

Key concepts

Aufbau Principle

The Aufbau Principle is a fundamental guideline used in quantum chemistry and atomic physics to determine the electron configuration of an atom. The principle's name comes from the German word 'aufbauen', meaning 'to build up'. It suggests that as we move up in atomic number, electrons are added one by one to the lowest energy orbitals available before moving to higher energy levels.

According to the Aufbau Principle, electrons occupy orbitals starting from the lowest available (which is the 1s orbital) and progress to higher energy levels in a specific sequence. This sequence reflects the order in which energy levels and sublevels are filled, and it is a crucial aspect for students to grasp when writing electron configurations. A commonly used shorthand to remember this order is: 1s, 2s, 2p, 3s, and so on.

Periodic Table

The periodic table is much more than just a table of elements; it's a powerful tool that reflects the periodicity and trends in properties of the elements based on their atomic structure. It is organized by increasing atomic number (number of protons in the nucleus) and arranged in such a way that elements with similar chemical properties fall into the same columns, known as groups or families.

For students learning about electron configurations, the periodic table helps visualize the patterns in which electrons are distributed around the nucleus and provides a handy reference for determining the atomic number, which is crucial for writing out electron configurations. Elements are also divided into blocks corresponding to their outermost electron subshells, such as the 's-block', 'p-block', 'd-block', and 'f-block', which align with the typical orbital filling order.

Atomic Number

The atomic number plays a pivotal role in determining an element's position in the periodic table and its electron configuration. It is equal to the number of protons found in the nucleus of an atom and by extension—thanks to the charge-neutral condition of atoms—it also equals the number of electrons orbiting the nucleus in a neutral atom. This simple number defines the unique identity of each element.

Understanding the significance of the atomic number is crucial when it comes to determining the filling order of electrons in an element's orbitals. For example, hydrogen, with an atomic number of 1, has just one electron that will occupy the first available orbital (1s), while carbon, with an atomic number of 6, will have its electrons fill up to the 2p orbital.

Orbital Filling Order

Orbital filling order refers to the sequence in which orbitals are populated with electrons. The ordering is based on the principle of increasing energy; orbitals that are lower in energy are filled before those that are higher in energy. This hierarchy originates from the quantum mechanics governing electron behavior and the shapes of atom's probability distributions.

The filling order is generally: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, and so on. It's important to note the exception that occurs after the 4s subshell; the 3d comes into play before the 4p, even though 'd' would normally suggest a higher energy level. This order of filling is key in predicting and understanding the electron configuration of elements, especially in transition metals and inner transition metals where the 'd' and 'f' subshells are involved.