Question

Write the full electron configuration \(\left(1 s^{2} 2 s^{2}, \text { etc. }\right)\) for each of the following elements. a. sodium, \(Z=11\) b. cesium, \(Z=55\) c. nitrogen, \(Z=7\) d. beryllium, \(Z=4\)

Short answer

a. Sodium: \(1s^2 2s^2 2p^6 3s^1\) b. Cesium: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1\) c. Nitrogen: \(1s^2 2s^2 2p^3\) d. Beryllium: \(1s^2 2s^2\)

Step-by-step solution

Start filling electrons

Follow the energy level order and fill electrons until the 11th electron is placed. Sodium has 11 electrons, so its configuration is: \(1s^2 2s^2 2p^6 3s^1\) b. Cesium, \(Z=55\)

Start filling electrons

Follow the energy level order and fill electrons until the 55th electron is placed. Cesium has 55 electrons, so its configuration is: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1\) c. Nitrogen, \(Z=7\)

Start filling electrons

Follow the energy level order and fill electrons until the 7th electron is placed. Nitrogen has 7 electrons, so its configuration is: \(1s^2 2s^2 2p^3\) d. Beryllium, \(Z=4\)

Start filling electrons

Follow the energy level order and fill electrons until the 4th electron is placed. Beryllium has 4 electrons, so its configuration is: \(1s^2 2s^2\)

Key concepts

Energy Levels

Energy levels, also known as electron shells, define the specific energy states in which electrons reside around an atom's nucleus. These levels can be imagined as concentric circles around the nucleus where electrons can orbit. Each level corresponds to a quantized energy value for the electron. When filling electrons in an atom, they are placed from lower to higher energy levels. This is known as the Aufbau principle.
The energy levels are denoted by principal quantum numbers (n=1, 2, 3, etc.), where the number indicates the distance of the shell from the nucleus. The closest shell is n=1, and it increases as electrons move further from the nucleus. As electrons fill these levels, they first occupy the lowest energy level available to them to achieve the most stable, low-energy, configuration.
To summarize:

• Energy levels are established by quantum numbers.
• Electrons fill these levels starting from the lowest (n=1).
• This filling of electrons follows a specific order based on energy values, depicted through the Aufbau principle.

Electron Placement

Electron placement follows a specific order. This order is determined by the energy of available orbitals. Electrons prefer to occupy the lowest energy orbital available. This is logical because systems generally favor stability, which usually occurs at lower energy states. The order of filling is typically noted as:

• 1s
• 2s, 2p
• 3s, 3p, 4s
• 3d, 4p, 5s
• 4d, 5p, 6s

However, it's important to note that due to their proximity in energy, 4s fills before 3d. When assigning electrons, you count them into these orbitals until all electrons an atom possesses have been placed. This results in the atom's electron configuration, like how sodium \(1s^2 2s^2 2p^6 3s^1\) is configured with its 11 electrons.
This method ensures organized placement of electrons around the nucleus, maximizing stability and minimizing energy.

Quantum Chemistry

Quantum chemistry is an essential branch of chemistry that uses principles of quantum mechanics to understand and predict molecular systems. It involves complex mathematics to determine electron distributions, also known as electron configurations, within atoms and molecules. Quantum chemistry explains why electrons reside in specific orbitals, and how their arrangement influences chemical properties.
This field of study describes electrons in terms of quantum states, which are solutions to the Schrödinger equation. This conceptual framework leads to the idea that electrons exist in clouds of probability rather than fixed pathways. These probabilistic zones are what we refer to as orbitals, and each has a distinct energy relieved in quantum terms.
Important aspects of quantum chemistry include:

• Understanding electron arrangements through principles like the Pauli Exclusion Principle, stating no two electrons can have the same set of quantum numbers.
• Predicting bond formation, electron sharing, and molecular shapes.
• Using quantum chemistry calculations to model chemical reactions.

By grasping its principles, you can better understand atomic interactions and the properties of elements.