(d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.

Verified step by step guidance

1. Step 1: The energy of an orbital in a hydrogen atom is determined by its principal quantum number (n). The larger the value of n, the higher the energy and less stability of the orbital.
2. Step 2: The principal quantum number (n) is the number that precedes the letter in the orbital notation. For example, in the 4f orbital, the principal quantum number is 4.
3. Step 3: Using the principal quantum number, we can order the orbitals from lowest to highest energy (most stable to least stable). In this case, the order would be 1s, 2p, 3d, 4f, 6s.
4. Step 4: Note that for a multi-electron atom, the energy of an orbital is determined by both the principal quantum number (n) and the azimuthal quantum number (l). However, for a hydrogen atom, only the principal quantum number (n) determines the energy of an orbital.
5. Step 5: Remember that the lower the energy of an orbital, the more stable it is. Therefore, the 1s orbital is the most stable, and the 6s orbital is the least stable in a hydrogen atom.

Key Concepts

Quantum Mechanics and Orbitals

Quantum mechanics describes the behavior of electrons in atoms, where electrons occupy regions of space called orbitals. Each orbital has a specific shape and energy level, which is determined by quantum numbers. Understanding the arrangement of these orbitals is crucial for predicting the stability and reactivity of atoms.

Aufbau Principle

The Aufbau principle states that electrons fill orbitals starting from the lowest energy level to the highest. This principle helps in determining the order of orbital filling, which is essential for understanding the electronic configuration of an atom. It guides the sequence in which orbitals are filled, impacting the atom's stability.

Energy Levels and Sublevels

Energy levels in an atom are divided into sublevels (s, p, d, f), each with a specific energy hierarchy. The order of increasing energy for these sublevels is influenced by their principal quantum number and the type of sublevel. Recognizing this hierarchy is vital for arranging orbitals in order of stability and energy.