Question

List the first five orbitals (the five orbitals in an atom at lowest energy) in order of filling, according to the Aufbau principle.

Short answer

1s, 2s, 2p, 3s, 3p.

Step-by-step solution

Understand the Aufbau Principle

The Aufbau principle states that electrons occupy the lowest energy orbitals first. This is a key principle in determining the order in which orbitals fill up.

List the Order Based on Increasing Energy

To identify the orbitals in order of energy, we use the n+l rule (where n is the principal quantum number and l is the azimuthal quantum number). Orbitals fill in the order of increasing n+l. For orbitals with the same n+l value, the one with the lower n fills first.

Determine the First Five Orbitals

Starting from the lowest, the order of filling is: 1. 1s (n=1, l=0 -> n+l=1) 2. 2s (n=2, l=0 -> n+l=2) 3. 2p (n=2, l=1 -> n+l=3) 4. 3s (n=3, l=0 -> n+l=3) 5. 3p (n=3, l=1 -> n+l=4)

Write Down the First Five Orbital Designations

Based on the analysis, the first five orbitals in order of filling are: 1s, 2s, 2p, 3s, and 3p. These orbitals represent the increasing energy levels from the nucleus outward.

Key concepts

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's orbitals. Think of it as the address of each electron within an atom. It helps us understand the arrangement and behavior of electrons around the nucleus. In practice, electron configuration is represented by a series of numbers and letters indicating sublevel and orbital information.
For example, the electron configuration for carbon is written as 1s² 2s² 2p². This notation shows us which orbitals electrons occupy and in what order. If we want to figure out the configuration for a particular element, we fill the orbitals with electrons following a specific order, determined by their energy levels. The Aufbau principle helps us determine this sequence.
Learning electron configuration provides insight into chemical properties and reactivity of elements. It is essential in predicting how atoms will bond and interact with each other.

Orbital Filling

Orbital filling refers to the order in which electrons populate orbitals within an atom. This is guided by a set of rules, with the Aufbau principle being one of the most crucial. The Aufbau principle states that electrons fill the lowest energy orbitals first before moving to higher energy ones.
In general, the filling order is determined using the n+l rule. According to this rule:

• The sum of the principal quantum number (n) and the azimuthal quantum number (l) determines the order.
• The orbital with the lowest n+l value is filled first.
• If two orbitals have the same n+l value, the one with the lower n value fills first.

This sequence ensures that electrons are arranged in the most stable and low-energy configuration possible, which is crucial for understanding chemical bonding and physical properties of elements.

Quantum Numbers

Quantum numbers are vital in describing the distribution of electrons in an atom. They provide important information about each electron's energy level, shape, and orientation of its orbital.
The four types of quantum numbers are:

• Principal Quantum Number (n): Indicates the energy level and size of the orbital. Higher 'n' means electrons are further from the nucleus.
• Azimuthal Quantum Number (l): Defines the shape of the orbital. It ranges from 0 to n-1.
• Magnetic Quantum Number (m_l): Indicates the orientation of the orbital in space. It ranges from -l to +l.
• Spin Quantum Number (m_s): Denotes the spin of the electron, which can be either +1/2 or -1/2.

These quantum numbers play a crucial role in determining an electron's position and movement within an atom. They help us predict how an atom interacts in bonding and its overall stability.

Energy Levels

Energy levels represent the specific energies that electrons can have within an atom. They are like steps of a ladder where electrons can "stand," but they cannot exist between these steps.
Each energy level corresponds to a set of quantum numbers that define the size, shape, and orientation of electron orbitals. Electrons on lower energy levels are closer to the nucleus and have less energy than those on higher levels. The principal quantum number (n) defines these levels, starting from n=1, which is the closest to the nucleus.
As we move to higher energy levels, orbitals become larger and more spaced out. The filling of these energy levels from low to high is critical for understanding the structure of atoms, as this orderly filling is dictated by the Aufbau principle. This hierarchy affects the chemical and physical properties of elements, helping explain periodic trends and bonding behavior in molecules.