Problem 24 - College Physics

Question

Identify the atoms of each of the following ground state electron configurations: (a) \(1 s^{2} 2 s^{2} ;\) (b) \(1 s^{2} 2 s^{2} 2 p^{3}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\)

Step-by-Step Solution

Answer

(a) Be; (b) N; (c) Ne; (d) S.

Step 1: Understand Electron Configuration

Electron configuration notation tells us how electrons are distributed in an atom's orbitals. Each superscript number indicates the number of electrons in a given subshell (s, p, d, f) for a specific principal quantum number (n=1, 2, 3,...).

Step 2: Identify Atom for Configuration (a)

For configuration (a) \(1s^2\ 2s^2\), sum the electrons: 2 (from \(1s^2\)) + 2 (from \(2s^2\)) = 4 electrons. This corresponds to beryllium (Be), which has an atomic number of 4.

Step 3: Identify Atom for Configuration (b)

For configuration (b) \(1s^2\ 2s^2\ 2p^3\), sum the electrons: 2 (from \(1s^2\)) + 2 (from \(2s^2\)) + 3 (from \(2p^3\)) = 7 electrons. This corresponds to nitrogen (N), which has an atomic number of 7.

Step 4: Identify Atom for Configuration (c)

For configuration (c) \(1s^2\ 2s^2\ 2p^6\), sum the electrons: 2 (from \(1s^2\)) + 2 (from \(2s^2\)) + 6 (from \(2p^6\)) = 10 electrons. This corresponds to neon (Ne), which has an atomic number of 10.

Step 5: Identify Atom for Configuration (d)

For configuration (d) \(1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^4\), sum the electrons: 2 (from \(1s^2\)) + 2 (from \(2s^2\)) + 6 (from \(2p^6\)) + 2 (from \(3s^2\)) + 4 (from \(3p^4\)) = 16 electrons. This corresponds to sulfur (S), which has an atomic number of 16.

Key Concepts

Atomic Number

The atomic number is a crucial aspect of understanding elements and their electron configurations. It represents the number of protons found in the nucleus of an atom. The atomic number is unique to each element, acting like an elemental fingerprint. For neutral atoms, which have no overall charge, the atomic number also indicates the number of electrons. For example, in configuration (a), there are 4 electrons in total. Thus, the atomic number is 4, which corresponds to Beryllium (Be).

• The atomic number defines the identity of an element.
• It is equal to the number of protons in a neutral atom.
• In electron configurations, it helps determine the specific element a configuration describes.

These aspects make the atomic number essential for identifying elements when presented with their electron configurations.

Principal Quantum Number

The principal quantum number, denoted as "n", plays a key role in electron configuration. It indicates the main energy level an electron resides in and largely determines an electron's energy and the size of an electron cloud. Each value of "n" corresponds to a shell in an atom where electrons can be found. For example:

• When "n" is 1, it refers to the first shell, closest to the nucleus.
• When "n" is 2, it denotes the second shell and so on.

The further away from the nucleus an energy level is, the higher its energy and the larger it is. In the configurations given, such as "1s" or "2s", the number before the letter denotes the principal quantum number, which helps us locate the electrons in different energy levels.

Subshell Notation

Subshell notation is a compact way to describe the distribution of electrons in an atom. It includes both the principal quantum number and the type of orbital (s, p, d, f) an electron is in, followed by a superscript number specifying how many electrons inhabit that particular subshell. Here's how to interpret it:

• "1s²" tells us there are 2 electrons in the s orbital of the first principal energy level (n=1).
• "2p³" indicates 3 electrons are placed in the p orbital of the second principal energy level (n=2).

This notation is critical for understanding how electrons are organized within an atom. With this information, you can easily identify which subshells are fully or partially filled, and thus determine the ground state configuration of atoms.

Ground State Electron Configuration

The ground state electron configuration of an atom is its most stable configuration, where electrons are organized in the lowest possible energy levels. Electrons fill the orbitals following the Aufbau principle, which states that electrons occupy the lowest energy orbital available. This principle helps explain the sequence of electron configurations:

• First, electrons fill the 1s orbital.
• Next, they move to 2s, followed by 2p, 3s, and so on according to increasing energy.

For example, in configuration (d) 1s² 2s² 2p⁶ 3s² 3p⁴, the electrons populate the lowest energy subshells available until all 16 electrons are placed. This minimizes the energy of the atom, representing its ground state. Understanding this concept ensures a clearer grasp on how atoms interact and form molecules.