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

Unpaired electrons are those that are alone in an orbital, not forming a pair with another electron with opposite spin. The presence of unpaired electrons is a central concept in chemistry because they are usually the electrons involved in chemical bonding and magnetic properties.

For instance, in the exercise given, Oxygen (O) has two unpaired electrons in its 2p orbitals. This impacts how Oxygen forms bonds with other atoms. Similarly, Chromium (Cr) has five unpaired electrons, which is quite unique and leads to its characteristic magnetic properties and chemical reactivity.

Identifying Unpaired Electrons

When identifying unpaired electrons, one must first understand the Pauli Exclusion Principle, stating that no two electrons in an atom can have identical quantum numbers. Therefore, an orbital can hold two electrons with opposite spins. Using the electron configuration, you can determine which orbitals are not fully occupied and count the unpaired electrons. A filled or half-filled orbital signals stability, while orbitals that are not fully occupied depict the number of unpaired electrons.

The periodic table is an organized chart of all known elements arranged according to their atomic number, electron configurations, and recurring chemical properties. Each element in the table is represented by its chemical symbol, and the elements are listed in order of increasing atomic number.

Elements in the same column, known as a group, typically have similar properties and electron configurations, especially in their outermost shells. Horizontal rows are called periods and indicate the energy levels of an atom's electrons.

Utilizing the Periodic Table

To solve problems such as determining the element with a given electron configuration, one starts at the top with Hydrogen (atomic number 1) and follows the elements in order until reaching the total number of electrons that matches the configuration. For example, Tellurium (Te), in step 7 of the exercise, can be identified using the periodic table by counting up to atomic number 52.

The atomic number of an element is the number of protons found in the nucleus of an atom, and it determines the chemical properties and place of an element in the periodic table. Since atoms are electrically neutral, the atomic number also equals the number of electrons in an uncharged atom.

The atomic number is fundamental when working with electron configurations. For example, the number of electrons in a neutral atom will be consistent with its atomic number. The step by step solution identifies elements such as Beryllium (Be) and Chromium (Cr) by matching the total electrons in the electron configuration to the atomic number of the element on the periodic table.

Importance of Knowing the Atomic Number

Understanding the atomic number aids in predicting how an element will react chemically. A lower atomic number typically means the element is more abundant and reactive, while a higher atomic number usually indicates the opposite. For instance, elements with an atomic number greater than 82 (Lead) are all radioactive.