Question

Identify the atom that has each ground-state electron configuration. (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) (b) \(1 s^{2} 2 s^{2} 2 p^{4}\)

Short answer

Question: Identify the atoms with the following ground-state electron configurations: (a) \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4}\) (b) \(1s^{2} 2s^{2} 2p^{4}\) Answer: (a) Sulfur (S) (b) Oxygen (O)

Step-by-step solution

Determine the total number of electrons in each electron configuration

To find the number of electrons in each configuration, simply multiply the principal quantum number (the lower subscript) by the second subscript and sum them up for all the orbitals in the configuration. (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) Here, we have the following orbitals and their respective electrons: \(1s^2\) = 2 electrons \(2s^2\) = 2 electrons \(2p^6\) = 6 electrons \(3s^2\) = 2 electrons \(3p^4\) = 4 electrons Total electrons = 2 + 2 + 6 + 2 + 4 = #tag_math# 16 #tag_math# electrons (b) \(1 s^{2} 2 s^{2} 2 p^{4}\) Here, we have the following orbitals and their respective electrons: \(1s^2\) = 2 electrons \(2s^2\) = 2 electrons \(2p^4\) = 4 electrons Total electrons = 2 + 2 + 4 = #tag_math# 8 #tag_math# electrons

Use the periodic table to identify the atoms

Now that we have the total number of electrons for both configurations, we can use the periodic table to find the corresponding elements by matching the number of electrons with the atomic number of an element (elements are organized by increasing atomic number). (a) 16 electrons: The element with an atomic number of 16 is #tag_math# \textbf{Sulfur (S)} #tag_math# (b) 8 electrons: The element with an atomic number of 8 is #tag_math# \textbf{Oxygen (O)} #tag_math#

Final Answer

The atoms with the given ground-state electron configurations are: (a) Sulfur (S) (b) Oxygen (O)

Key concepts

Ground-State Electron Configuration

The ground-state electron configuration of an atom reveals the arrangement of electrons in its most stable, lowest energy form. Electrons fill sublevels in the order of increasing energy, from lower to higher energy orbitals. This is explained by the Aufbau principle which guides the sequential filling of orbitals starting from the lowest energy level.
In the examples provided, the configurations represent the following fillings: for (a) sulfur, the electrons fill up the 1s, 2s, 2p, 3s, and 3p orbitals; for (b) oxygen, the filling stops at the 2p orbital. The superscripts represent how many electrons are in each orbital, and their sum gives the total number of electrons, which is crucial for identifying the element. Understanding the ground-state electron configuration is essential for studying chemical bonding, predicting molecule shapes, and chemical behavior.
For students looking to improve their grasp of this concept, it is helpful to memorize the order of orbital filling and to practice with numerous elements from the periodic table to solidify their understanding.

Quantum Numbers

Quantum numbers give a detailed description of an electron's position and behavior within an atom. There are four quantum numbers: the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).

• The principal quantum number (n) indicates the main energy level or shell, and its value can be any positive integer.
• The angular momentum quantum number (l) defines the shape of the orbital, with values ranging from 0 to (n-1).
• The magnetic quantum number (m_l) specifies the orientation of the orbital in space and can take on values from -l to +l.
• The spin quantum number (m_s) indicates the direction of the electron's spin and can either be +1/2 or -1/2.

These numbers are derived from the solutions to the Schrödinger equation and are fundamental to the concept of orbitals. Grasping quantum numbers helps one understand why electrons occupy specific orbitals and how electron configurations are constructed.

Periodic Table

The periodic table is a comprehensive chart that organizes all the chemical elements based on their atomic numbers (number of protons), electron configurations, and recurring chemical properties. It’s divided into periods (horizontal rows) and groups or families (vertical columns). Elements in the same group often share similar properties, such as valence electron counts, which dictate their chemical reactivity.
For instance, when identifying an element by its ground-state electron configuration, as in the exercise, the periodic table becomes an indispensable tool. By knowing that the atomic number corresponds to the number of protons (and, in a neutral atom, the number of electrons), a student can match the total electrons from an electron configuration to the atomic number on the periodic table and thereby identify the element. Familiarizing oneself with the layout of the periodic table, including the s, p, d, and f blocks, greatly aids in visualizing the electron fill order and can immensely improve one’s understanding of how elements relate to each other chemically and physically.