Question

Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) \(1 s^{2} 2 s^{2}\), (b) \(1 s^{2} 2 s^{2} 2 p^{4}\) (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\) (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\)

Short answer

(a) The element corresponding to \(1s^2 2s^2\) is Beryllium (Be), and it has 0 unpaired electrons. (b) The element corresponding to \(1s^2 2s^2 2p^4\) is Oxygen (O), and it has 2 unpaired electrons. (d) The element corresponding to \([\mathrm{Kr}] 5s^2 4d^{10} 5p^4\) is Tellurium (Te), and it has 2 unpaired electrons. (c) The element corresponding to \([\mathrm{Ar}] 4s^1 3d^5\) is Chromium (Cr), and it has 6 unpaired electrons.

Step-by-step solution

(a) Identify the element corresponding to \(1s^2 2s^2\)

To identify the element, we need to count the total number of electrons based on its electron configuration. In this case, \(1s^2\) indicates that there are 2 electrons in the \(1s\) subshell and \(2s^2\) indicates there are 2 electrons in the \(2s\) subshell. Thus, the total number of electrons is 2 + 2 = 4. Now, we look at the periodic table and find an element with an atomic number (number of protons) of 4, which corresponds to Beryllium (Be).

(a) Determine the number of unpaired electrons for \(1s^2 2s^2\)

Since all orbitals in the configuration are fully filled (s-orbitals can contain 2 electrons), there are no unpaired electrons.

(b) Identify the element corresponding to \(1s^2 2s^2 2p^4\)

Count the total number of electrons: 2 (from \(1s^2\)) + 2 (from \(2s^2\)) + 4 (from \(2p^4\)) = 8. Looking at the periodic table, an atomic number of 8 corresponds to Oxygen (O).

(b) Determine the number of unpaired electrons for \(1s^2 2s^2 2p^4\)

Here, the p-orbital has a maximum capacity of 6 electrons, and there are 4 in the configuration \(2p^4\). Two of the electrons are unpaired (since each p-orbital can hold 2 electrons). Thus, there are 2 unpaired electrons.

(d) Identify the element corresponding to \([\mathrm{Kr}] 5s^2 4d^{10} 5p^4\)

First, we need to determine the electron configuration of the noble gas Kr. Kr stands for Krypton, which has an atomic number of 36. Now, we add the electrons in the rest of the configuration: 2 (from \(5s^2\)) + 10 (from \(4d^{10}\)) + 4 (from \(5p^4\)) = 16 electrons. Adding these to the 36 electrons of Kr, we get 52 electrons in total. Referencing the periodic table, an atomic number of 52 corresponds to Tellurium (Te).

(d) Determine the number of unpaired electrons for \([\mathrm{Kr}] 5s^2 4d^{10} 5p^4\)

All the electrons in subshells \(5s\) and \(4d\) are paired, but there are 2 unpaired electrons in the \(5p\) subshell (out of a maximum of 6 electrons, 4 are present).

(c) Identify the element corresponding to \([\mathrm{Ar}] 4s^1 3d^5\)

Determine the electron configuration of the noble gas Ar. Ar stands for Argon, which has an atomic number of 18. Now, we add the electrons in the rest of the configuration: 1 (from \(4s^1\)) + 5 (from \(3d^5\)) = 6 electrons. Adding these to the 18 electrons of Ar, we get 24 electrons in total. The periodic table shows that an atomic number of 24 corresponds to Chromium (Cr).

(c) Determine the number of unpaired electrons for \([\mathrm{Ar}] 4s^1 3d^5\)

There is 1 unpaired electron in the \(4s\) subshell and 5 unpaired electrons in the \(3d\) subshell. Therefore, a total of 6 unpaired electrons exist for this element. Summary of the results: (a) Beryllium (Be), 0 unpaired electrons (b) Oxygen (O), 2 unpaired electrons (d) Tellurium (Te), 2 unpaired electrons (c) Chromium (Cr), 6 unpaired electrons

Key concepts

Unpaired Electrons

Unpaired electrons refer to electrons that are alone in an atomic or molecular orbital. Unlike paired electrons, these electrons do not share their orbital space with another electron of opposite spin. Understanding unpaired electrons is important because they often play a key role in determining the magnetic properties and reactivity of an element.

In chemistry, knowing the number of unpaired electrons helps predict the chemical behavior and magnetism of atoms or molecules.

• Paired electrons: Occupy the same orbital with opposite spins, leading to a stable, lower energy state.
• Unpaired electrons: Increase the energy but enable chemical bonding and reactions due to their ability to pair with other electrons.

To find unpaired electrons, look at the electron configuration of the element. Subshells like p, d, and f can hold multiple electrons and therefore can have unpaired electrons if partially filled. In our example, electrons in the p and d subshells often result in unpaired electrons. For instance, in oxygen (\(1s^2 2s^2 2p^4\)), the p subshell has two unpaired electrons, which contributes to its reactive nature.

Atomic Number

The atomic number is a fundamental concept in chemistry, representing the number of protons in the nucleus of an atom. It determines the identity of the element and its position on the periodic table. The atomic number is unique for each element and remains constant. As such, it is a key driver for classification.

• Defines the element: Each element has a unique atomic number, which dictates its characteristics and chemical properties.
• Corresponds with electrons: In a neutral atom, the number of protons (atomic number) equals the number of electrons.

When determining which element an electron configuration corresponds to, count the total number of electrons. This equates to the atomic number. For example, an electron configuration of \(1s^2 2s^2\) has a total of four electrons, matching the atomic number of Beryllium.

Periodic Table

The periodic table is an organized chart of elements arranged by increasing atomic number and by their chemical properties. It provides a comprehensive framework for understanding element properties, electron configurations, and their trends across periods and groups.

• Rows (Periods): Indicate increasing energy levels and repeated patterns in element properties.
• Columns (Groups): Elements with similar chemical properties and valence electron configurations.
• Blocks (s, p, d, f): Groupings based on electron configurations and subshell filling.

By referencing the periodic table, we can quickly identify an element from its atomic number or electron configuration. It's a vital tool for chemists and students alike, simplifying the complex nature of elemental behavior. In our exercise, using the atomic number derived from the electron configuration lead us to correctly identify Beryllium and other elements.

Beryllium

Beryllium is a chemical element with the symbol 'Be' and atomic number 4. It falls under the category of alkaline earth metals, which are found in group 2 of the periodic table.

Be has a relatively simple electron configuration, \(1s^2 2s^2\), with no unpaired electrons, making it stable and less reactive compared to some other elements. This element is known for its strong, lightweight, and corrosion-resistant properties, making it useful in aerospace and other industries.

• Atomic Number: 4
• Electron Configuration: \(1s^2 2s^2\)
• Unpaired Electrons: 0

Understanding beryllium's placement on the periodic table and its electron configuration helps us better appreciate its behavior and applications in different fields.