Problem 173 - Introductory Chemistry Atoms First

Question

What are the group number, period number, and name of the element whose electron configuration is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2} ?\)

Step-by-Step Solution

Answer

The element with the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2}\) is germanium (Ge), which has a group number of 14 and a period number of 4.

Step 1: Determine the highest energy level

The highest energy level (or principal quantum number) can be found by looking at the largest coefficient in the electron configuration. In this case, the highest energy level is 4.

Step 2: Count the valence electrons

Next, we'll count the number of valence electrons by finding the number of electrons in the outermost energy level. This electron configuration is: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2}\). The valence electrons are in the 4th energy level, and there are 2 electrons in the \(4s\) orbital and 2 electrons in the \(4p\) orbital. So there are a total of \(2 + 2 = 4\) valence electrons.

Step 3: Determine the group number

Since the element has 4 valence electrons, it is in Group 14 of the periodic table.

Step 4: Determine the period number

The highest energy level (principal quantum number) is 4, as determined in step 1. This corresponds to the element being in Period 4 of the periodic table.

Step 5: Identify the element

With a group number of 14 and a period number of 4, the element we're looking for is germanium (Ge). So the answer is:

Step 6: Group number

14

Step 7: Period number

4

Step 8: Element name

Germanium (Ge

Key Concepts

Valence Electrons

Valence electrons are the electrons that are present in the outermost shell of an atom. These electrons play a crucial role in determining how an element will react with others. In the context of the electron configuration, valence electrons are specifically those found in the highest principal quantum level. For the electron configuration given in the problem, \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2}\), the valence electrons are located in the 4s and 4p orbitals of the fourth shell.

To figure out the number of valence electrons, add up the electrons from the highest energy level. Here, it's the fourth level, which includes 2 electrons from the 4s orbital and 2 more from the 4p orbital, resulting in a total of 4 valence electrons.

Understanding valence electrons is key to predicting chemical behavior. They are essential for forming bonds with other atoms. In this configuration, the 4 valence electrons hint that the element is likely to form covalent bonds by sharing electrons with other atoms.

Periodic Table

The periodic table is a tabular arrangement of the chemical elements organized by increasing atomic number, electron configurations, and recurring chemical properties. Each element is placed in a specific position based on its atomic structure.

The group number of an element on the periodic table reveals important information about its valence electrons. Elements in the same group have a similar number of valence electrons, which gives them similar chemical properties. For the element we've assessed, having 4 valence electrons places it in Group 14.

Period numbers on the periodic table refer to the principal quantum number or the highest energy level of the electrons in an atom. It signifies the number of shells or energy levels an atom's electrons occupy. In this problem, the electron configuration suggests that the element is in Period 4, since the highest energy shell with electrons is the fourth (with the 4s and 4p orbitals).

Thus, the element with this configuration is germanium, which resides in Period 4 and Group 14, sharing properties with other Group 14 elements like silicon and tin.

Quantum Numbers

Quantum numbers are numbers assigned to each electron in an atom that describe its energy, shape, and orientation of its orbital. They define the position and state of an electron more thoroughly than classical physics allows.

The principal quantum number, denoted as \(n\), indicates the main energy level occupied by the electron. In electron configurations, this is represented by the largest number preceding each orbital type. For the given electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2}\), the principal quantum number reaches 4, signaling the highest energy level.

The angular momentum quantum number, \(l\), specifies the shape of the orbital and is dependent on the principal quantum number. Orbitals include s, p, d, and f types: s has \(l = 0\), p has \(l = 1\), and d has \(l = 2\). These numbers are visible in the electron configuration (e.g., s in 4s and p in 4p).

Lastly, understanding these quantum numbers aids in predicting an element’s bonding and electromagnetic properties, such as its likely ionic charge or magnetic behavior, further explaining the unique aspects of an element like germanium.