Question

List the hydrogen orbitals in increasing order of energy.

Short answer

The hydrogen orbitals in order of increasing energy are 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.

Step-by-step solution

Understand Atomic Orbitals

Atomic orbitals describe regions around the nucleus where electrons are likely to be found. They include s, p, d, and f orbitals, each with different shapes and energy levels.

Identify Principal Quantum Number (n)

The principal quantum number, denoted as 'n', indicates the main energy level or shell. For hydrogen, the orbitals with the same 'n' have similar energies, but they increase with higher 'n' values.

Examine the Energy Levels

For the hydrogen atom, the energies of orbitals depend solely on the principal quantum number 'n'. Hence, for a given 'n', orbitals s, p, d, and f within that energy level have the same energy.

List Orbitals by Increasing n

The order of energy for hydrogen orbitals based on 'n' is 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f. Orbital energies increase with increasing 'n', and within the same 'n', they have equal energy.

Final Ordering of Hydrogen Orbitals

The list of hydrogen orbitals in order of increasing energy is: 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and so on, continuing with higher 'n' levels.

Key concepts

Atomic Orbitals

Imagine an electron as buzzing around the nucleus of an atom within a certain region. This region is called an atomic orbital. Atomic orbitals tell us where an electron is likely to be found most of the time.
Atomic orbitals are like clouds with distinct shapes and sizes depending on their type. There are several kinds, including:

• s-orbitals: They are spherical in shape.
• p-orbitals: They resemble dumbbells and have three orientations in space.
• d-orbitals: These have more complex shapes with five orientations.
• f-orbitals: These have even more complex shapes with seven orientations.

Each orbital can hold a certain number of electrons due to quantum mechanics. For instance, s-orbitals can hold up to 2 electrons, while p-orbitals can accommodate up to 6. Understanding atomic orbitals helps us predict where electrons reside in an atom.

Principal Quantum Number

The principal quantum number, represented by the letter 'n', is like a label for the energy level of an electron within an atom. Think of it as a number that tells us the size of the electron's path around the nucleus.
It's akin to an address system, labeling each energy shell. The principal quantum number can only be a positive integer (1, 2, 3, ...). Here are some essential points:

• Larger 'n' values mean the orbital is further from the nucleus.
• As 'n' increases, the electron's energy also rises.
• In hydrogen, the orbitals are organized such that orbitals with the same 'n' have the same energy.

The variety in 'n' values is critical in determining the arrangement of electrons and understanding how atoms bond in chemical reactions.

Energy Levels

Energy levels in hydrogen's orbitals are mainly determined by the principal quantum number 'n'. Unlike large atoms, where sublevels within the same shell can differ in energy, hydrogen simplifies this. For hydrogen, each energy level has:

• All orbitals in the same 'n' level having the same energy.
• Increasing energy with larger 'n'.

Let's break this down further. In hydrogen, the energy of orbitals follows a pattern:
1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f.
For each increasing value of 'n', the orbitals carry the electrons further from the nucleus and to higher energy states. This predictable energy pattern helps chemists understand and predict chemical behavior.

s, p, d, and f Orbitals

The different types of orbitals—s, p, d, and f—are characterized by their shapes and the number of orientations they can have:

• s-orbitals: Only one orientation, spherical, capable of holding 2 electrons.
• p-orbitals: Three orientations, dumbbell-shaped, capable of holding 6 electrons in total.
• d-orbitals: Five orientations with complex clover shapes, capable of holding 10 electrons.
• f-orbitals: Seven orientations with even more complex shapes, holding up to 14 electrons.

These orbitals organize electrons in such a way that they minimize energy and maintain the stability of the atom. Electrons first fill the lower energy s-orbitals, then p, followed by d and f, as they seek the most stable, lowest energy configuration. Understanding these orbital types gives insight into the electron configuration and properties of elements in the periodic table.