Problem 74 - Chemistry: The Central Science

Question

The following electron configurations represent excited states. Identify the element, and write its ground-state condensed electron configuration. (a) \(\mathrm{ls}^{2} 2 \mathrm{~s}^{2} 3 p^{2} 4 p^{1}\), (b) \([\mathrm{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\), (c) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\)

Step-by-Step Solution

Answer

The ground-state condensed electron configurations for the given excited electron configurations are: a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\)

Step 1: Count electrons in the excited state

For each subshell, count the electrons and add them up. a) \(1s^{2} 2s^{2} 3p^{2} 4p^{1}\): 2 + 2 + 2 + 1 = 7 electrons b) \([\mathrm{Ar}] 3d^{10} 4s^{1} 4p^{4} 5s^{1}\): 18 (Ar) + 10 + 1 + 4 + 1 = 34 electrons c) \([\mathrm{Kr}] 4d^{6} 5s^{2} 5p^{1}\): 36 (Kr) + 6 + 2 + 1 = 45 electrons

Step 2: Identify elements in the periodic table

Based on the total number of electrons, we can find the corresponding elements. a) Element with 7 electrons: Nitrogen (N) b) Element with 34 electrons: Selenium (Se) c) Element with 45 electrons: Rhodium (Rh)

Step 3: Write ground-state condensed electron configurations

Write the ground-state electron configurations for the identified elements in condensed form. a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\) In conclusion, the ground-state condensed electron configurations for the given excited electron configurations are: a) Nitrogen (N): \(1s^{2} 2s^{2} 2p^{3}\) b) Selenium (Se): \([\mathrm{Ar}] 3d^{10} 4s^{2} 4p^{4}\) c) Rhodium (Rh): \([\mathrm{Kr}] 4d^{7} 5s^{1}\)

Key Concepts

Excited State

Atoms exist in different energy levels, and the arrangement of electrons can change due to energy absorption. When an electron in an atom absorbs energy, it can move to a higher energy level. This energy-driven change in electron configuration results in what we call an 'excited state'. It is important to note that excited states are not stable and are temporary until the electron returns to its original, lower energy level. This return process often results in the release of energy, typically in the form of light.

• In an excited state, electrons are in higher energy orbitals than in their most stable positions.
• It's the absorption of additional energy that causes electrons to jump up to higher levels.
• Excited states are useful in understanding phenomena such as atomic spectra and chemical reactions.

Ground-State Electron Configuration

The ground-state electron configuration is the arrangement of electrons in an atom at its lowest energy state. Essentially, this is how electrons naturally distribute among the various atomic orbitals when the atom is not energized. Determining the ground-state configuration provides a baseline for identifying any excited states. In a ground-state configuration, electrons fill orbitals starting from the lowest energy level and moving upward. The typical order follows the Aufbau principle, Hund's Rule, and Pauli Exclusion Principle, which help to explain the filling process.

• Aufbau Principle: Electrons occupy the lowest energy orbitals available.
• Hund's Rule: Electrons fill degenerate orbitals singly before pairing up.
• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

Periodic Table

The periodic table is a vital tool for understanding electron configurations. It not only organizes elements in order of increasing atomic number but also groups them by their chemical properties, which relate closely to their electron configurations. Each row, or period, in the table reflects a filling of a particular electron shell, while each column, or group, generally shares common valence electron configurations. Understanding the periodic table allows you to predict the electron configuration of any given element and identify trends in atomic radii, electronegativity, and ionization energy. For example:

• Elements in the same group often have similar valence electron configurations.
• Moving left to right across a period, the atomic number increases, adding electrons sequentially.
• The periodic table is divided into blocks (s, p, d, and f) based on the subshell that is being filled.

Electrons

Electrons are negatively charged particles that revolve around the nucleus of an atom in various orbitals. These tiny particles play a crucial role in chemical bonding and reactions, since they can be shared, transferred, or rearranged between atoms. Their distribution in the atomic orbitals determines the chemical behavior and properties of an element. Here are a few key points:

• Electrons reside in energy levels or shells around the nucleus, where each shell can hold a specific maximum number of electrons.
• Electron configurations determine the atom's state—in particular, whether it is in an excited or ground state.
• Changes in electron configuration, especially in the outermost electrons (valence electrons), are what drive chemical reactions.

Electrons are dynamic and key to understanding not just chemical identities, but also processes such as electricity, magnetism, and light interactions.