(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.

Verified step by step guidance

1. Identify the principal quantum number (n) for each orbital, which indicates the energy level. For example, in the 3s orbital, n=3.
2. Recognize that for a hydrogen atom, the energy of an orbital primarily depends on the principal quantum number (n). Orbitals with a lower n value have lower energy.
3. Arrange the orbitals by their principal quantum number (n) in ascending order. If two orbitals have the same n value, they have the same energy in a hydrogen atom.
4. List the orbitals in order from the lowest n value to the highest n value. Since all orbitals with the same n value have the same energy in hydrogen, they can be listed in any order within the same n value.
5. Final order from lowest to highest energy for the hydrogen atom will be: 2s, 2p, 3s, 4d, 5s.

Key Concepts

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them. The principal quantum number (n) indicates the energy level, while the azimuthal quantum number (l) defines the shape of the orbital. For example, s orbitals have l=0, p orbitals have l=1, and d orbitals have l=2. Understanding these numbers is essential for determining the energy hierarchy of orbitals.

Aufbau Principle

The Aufbau principle states that electrons occupy the lowest energy orbitals first before filling higher energy levels. This principle guides the order in which orbitals are filled in an atom, which is crucial for determining the electron configuration. For hydrogen, the order of increasing energy for the given orbitals follows this principle, allowing us to rank them accurately.

Energy Levels and Sublevels

Energy levels in an atom are divided into sublevels (s, p, d, f) that have different energy states. The energy of these sublevels increases with the principal quantum number and the type of sublevel. For instance, within the same principal level, p orbitals are higher in energy than s orbitals, and d orbitals are higher than p orbitals. This hierarchy is essential for ordering the given orbitals by energy.