Question

The electron configurations described in this chapter all refer to gaseous atoms in their ground states. An atom may absorb a quantum of energy and promote one of its electrons to a higher-energy orbital. When this happens, we say that the atom is in an excited state. The electron configurations of some excited atoms are given. Identify these atoms and write their groundstate configurations: (a) \(1 s^{1} 2 s^{1}\) (b) \(1 s^{2} 2 s^{2} 2 p^{2} 3 d^{1}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 4 s^{1}\) (d) \([\mathrm{Ar}] 4 s^{1} 3 d^{10} 4 p^{4}\) (e) \([\operatorname{Ne}] 3 s^{2} 3 p^{4} 3 d^{1}\)

Short answer

(a) He: \(1s^2\), (b) C: \(1s^2 2s^2 2p^2\), (c) Na: \(1s^2 2s^2 2p^6 3s^1\), (d) Se: \([Ar] 4s^2 3d^{10} 4p^4\), (e) S: \([Ne] 3s^2 3p^4\).

Step-by-step solution

Analyze Excited State Configuration (a)

The given configuration is \(1s^1 2s^1\). In an excited state, an electron is promoted to a higher orbital. Here, we notice that only the \(1s\) electron is normally fully filled for hydrogen. Therefore, the ground state should be \(1s^2\), corresponding to Helium (He) with an electron displaced to the 2s orbital in the excited state. So, the ground state configuration for \(1s^1 2s^1\) is \(1s^2\).

Analyze Excited State Configuration (b)

The configuration is \(1s^2 2s^2 2p^2 3d^1\). Normally, electrons fill the 2p orbital before moving to the 3d. But, here we have three \(2p\) present and one excited to the 3d orbital. This looks like boron \(1s^2 2s^2 2p^1\) in ground state plus the electron promoted to a 3d orbital. Thus, the ground state is error in assumption, more electrons are present, we look at carbon \(1s^2 2s^2 2p^2\) promoted to 3d, unchanged \(1s^2 2s^2 2p^2\) fits , response in ground \(1s^2 2s^2 2p^2\).

Analyze Excited State Configuration (c)

The configuration is \(1s^2 2s^2 2p^6 4s^1\). The 3s orbital should normally fill before electrons advance to the 4s level. This pattern arises when the 3s electron is excited to 4s. It aligns with sodium (Na), whose ground state is \(1s^2 2s^2 2p^6 3s^1\). Hence, \(1s^2 2s^2 2p^6 3s^1\) is the ground state configuration.

Analyze Excited State Configuration (d)

The configuration is \([\mathrm{Ar}] 4s^1 3d^{10} 4p^4\). Normally, 4s and 3d should fill before 4p. The excited 4s electron points us to the Kr atom with a ground state \([\mathrm{Ar}] 4s^2 3d^{10} 4p^3\), which should be \([\mathrm{Ar}] 4s^2 3d^{10} 4p^6\), too many electrons so actually like Se \([\mathrm{Ar}] 4s^2 3d^{10} 4p^4\), no d. possibly external excess accidental note except\([\mathrm{Ar}] 4s^2 3d^{10} 4p^4\) instead wasn't checked, equal dps, configuration elements ensure.

Analyze Excited State Configuration (e)

The configuration is \([\mathrm{Ne}] 3s^2 3p^4 3d^1\). Under normal circumstances the electron should fill via the third energy level, stopping before 3d. The excited state here indicates sulfur(S) in ground state \([\mathrm{Ne}] 3s^2 3p^4\) and an extra electron pushed further. Hence, the ground state configuration is \([\mathrm{Ne}] 3s^2 3p^4\).

Key concepts

Ground State

The ground state of an atom is its most stable form, where all electrons occupy the lowest possible energy levels or orbitals. Electrons fill these orbitals according to the principle known as the "Aufbau principle," which states that electrons are added to the lowest energy levels first. In the ground state, atoms are in their naturally occurring configuration, where they are most stable and exhibit the least amount of energy. This state is highly significant because it serves as the foundation for predicting electronic behavior in chemical reactions.

Electrons will organize themselves based on the energy levels allotted for each orbital, with lower energy levels being filled before higher ones. The configuration is typically written using a series of numbers and letters, elucidating how many electrons populate each level. For example, in the ground state configuration of carbon, the configuration is written as:

• The number before the letter represents the energy level (e.g., 1, 2, 3...)
• The letter (s, p, d, f) indicates the type of orbital the electrons occupy.
• The superscript shows how many electrons are in that orbital.

Excited State

When an atom absorbs energy, it can achieve the excited state. This usually involves shifting an electron from a lower energy orbital to a higher one. Unlike the ground state, the excited state is temporary and often leads to instability. An electron in an excited state can fall back to a lower energy level, releasing energy as heat or light in the process.

Transforming an atom from a ground state to an excited state involves the absorption of a specific quantum of energy. This energy shift allows us to explore phenomena like how certain substances emit light (as seen in fireworks) or the photoluminescence of elements. Excited states play a crucial role in fields such as spectroscopy and chemistry, as understanding them helps in identifying various materials based on their emission or absorption spectra.

• Electrons jump to higher energy levels.
• The configuration changes to reflect higher energy states.
• This state is pivotal for understanding chemical reactivity and bonding.

Quantum Theory

The quantum theory forms the backbone of our understanding of electron configuration and behaviors of atoms. It provides a framework explaining how microscopic particles like electrons behave, offering insights into the nature of chemical bonds and atomic structures.

Quantum theory introduces core concepts like energy levels, probability clouds, and quantum numbers that are crucial in determining how electrons are distributed in an atom. Electrons obey the Pauli Exclusion Principle, which means no two electrons in an atom can have the same set of quantum numbers. This explains why electrons in an atom fill distinct orbitals.

• Quantum numbers provide a system to describe the distribution and energy of electrons.
• Energy levels and sublevels are defined, helping to predict electron positions.
• Probability clouds determine regions where electron presence is most likely.

These concepts are not only essential in fundamental chemistry but are also vital in technologies such as semiconductors and quantum computing, showing how influential quantum theory is in both understanding and applying chemical properties.

Orbital Filling

Orbital filling is the process through which electrons are distributed among the various orbitals around an atom's nucleus. The rules governing this distribution are crucial to understanding the properties and chemical behaviors of elements.

According to the Aufbau principle, electrons fill orbitals starting from the lowest available energy levels to the highest. Closely related is Hund's Rule, which states electrons will fill an empty orbital before they pair up in an already occupied one, due to electronic repulsion. Meanwhile, the Pauli Exclusion Principle ensures no two electrons in a single atom can have identical quantum numbers.

• Electrons fill orbitals based on increasing energy.
• Hund's Rule optimizes electron distribution by minimizing repulsion.
• Electrons in the same orbital must have opposite spins, as dictated by the Pauli Exclusion Principle.

Orbital filling patterns give each element its unique set of characteristics, driving its place on the periodic table and guiding its potential reactions with other substances.