Problem 80 - Chemistry: The Central Science in SI Units, Global Edition

Question

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

Step-by-Step Solution

Answer

The short answer based on the provided solution is: (a) Fluorine (F): \(1 s^2 2 s^2 2 p^6 3 s^1\) (b) Sulfur (S): \([\mathrm{Ne}]3 s^2 3 p^6\) (c) Cobalt (Co): \([\mathrm{Ar}] 4 s^2 3 d^{10} 4 p^1\)

Step 1: (a) Find the total number of electrons

For the given excited state configuration, \(1 s^2 2 s^2 2 p^4 3 s^1\), let's find the total number of electrons. \(1 s^2\) = 2 electrons \(2 s^2\) = 2 electrons \(2 p^4\) = 4 electrons \(3 s^1\) = 1 electron Total number of electrons = 2 + 2 + 4 + 1 = 9 electrons

Step 2: (a) Write the ground-state electron configuration

For 9 electrons, the ground-state electron configuration is: \(1 s^2 2 s^2 2 p^6 3 s^1\)

Step 3: (a) Identify the element

The element with an atomic number (number of protons and electrons) of 9 is fluorine (F).

Step 4: (b) Find the total number of electrons

For the given excited state configuration, \([\mathrm{Ne}] 3 s^1 3 p^4 4 p^1\), let's find the total number of electrons. Neon (Ne) has 10 electrons, so we start there and add the electrons from the configuration. \(3 s^1\) = 1 electron \(3 p^4\) = 4 electrons \(4 p^1\) = 1 electron Total number of electrons = 10 (Ne) + 1 + 4 + 1 = 16 electrons

Step 5: (b) Write the ground-state electron configuration

For 16 electrons, the ground-state electron configuration is: \([\mathrm{Ne}]3 s^2 3 p^6\)

Step 6: (b) Identify the element

The element with an atomic number of 16 is sulfur (S).

Step 7: (c) Find the total number of electrons

For the given excited state configuration, \([\mathrm{Ar}] 4 s^2 3 d^6 4 p^1\), let's find the total number of electrons. Argon (Ar) has 18 electrons, so we start there and add the electrons from the configuration. \(4 s^2\) = 2 electrons \(3 d^6\) = 6 electrons \(4 p^1\) = 1 electron Total number of electrons = 18 (Ar) + 2 + 6 + 1 = 27 electrons

Step 8: (c) Write the ground-state electron configuration

For 27 electrons, the ground-state electron configuration is: \([\mathrm{Ar}] 4 s^2 3 d^{10} 4 p^1\)

Step 9: (c) Identify the element

The element with an atomic number of 27 is cobalt (Co). To summarize, the ground-state condensed electron configurations for the given excited state configurations are: (a) Fluorine (F): \(1 s^2 2 s^2 2 p^6 3 s^1\) (b) Sulfur (S): \([\mathrm{Ne}]3 s^2 3 p^6\) (c) Cobalt (Co): \([\mathrm{Ar}] 4 s^2 3 d^{10} 4 p^1\)

Key Concepts

Excited States

Atoms can absorb energy, causing their electrons to move to higher energy levels. This temporary state is known as the 'excited state'. Unlike the stable 'ground state', the excited state is fleeting as electrons tend to fall back to their lower energy levels, emitting energy in the process.
Understanding the excited states is crucial because it allows us to recognize how electrons behave when they gain energy, such as during chemical reactions or light absorption. Here's a simple breakdown to grasp this concept:

• Electrons gain energy and jump to higher energy orbits.
• This state is often unstable and temporary.
• When returning to ground state, electrons release energy.

When analyzing electron configurations, identifying if an atom is in an excited state can help predict chemical behaviors and reactions.

Ground-State Configurations

The ground-state electron configuration represents the most stable arrangement of electrons in an atom. In this state, electrons occupy the lowest possible energy levels. Electrons fill orbitals in a specific sequence, adhering to rules such as the Aufbau principle, Hund's rule, and the Pauli exclusion principle. These rules help determine the order and manner in which electrons fill orbitals:

• Aufbau Principle: Electrons fill from lower to higher energy levels.
• Hund's Rule: Electrons will fill degenerate orbitals singly before pairing.
• Pauli Exclusion Principle: Each orbital can accommodate two electrons with opposite spins.

The ground-state configuration provides a fundamental basis for predicting how elements will interact and bond with others.

Periodic Table

The periodic table is a vital tool for understanding the properties and behaviors of elements. It organizes elements based on their atomic number and recurring chemical properties, allowing us to see trends across different elements. The layout of the periodic table helps determine electron configurations and, ultimately, chemical reactivity.
Some essential features of the periodic table include:

• Groups: Vertical columns that identify elements with similar chemical behaviors.
• Periods: Horizontal rows that indicate increasing atomic numbers.
• Blocks: s, p, d, and f blocks represent the electron orbitals being filled by elements.

Mastering the periodic table is key to understanding electron configurations, as it directly informs the order in which electrons occupy atomic orbitals.

Atomic Number

The atomic number is fundamental in identifying elements. It represents the number of protons in an atom's nucleus and is the unique identifier for each element on the periodic table.
The atomic number also denotes the number of electrons in a neutral atom, which helps us with the electron configuration. Here are some of its key roles:

• Determines the identity of an element.
• Correlates with an element's position on the periodic table.
• Influences the chemical behavior and properties of an element.

Understanding the atomic number is essential for writing electron configurations, predicting element properties, and identifying elements based solely on their protons or electron count.