Question

For each element, count the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) carbon, (b) phosphorus, (c) neon.

Short answer

In their ground state, (a) Carbon (C) has 4 valence electrons, 2 core electrons, and 2 unpaired electrons; (b) Phosphorus (P) has 5 valence electrons, 10 core electrons, and 3 unpaired electrons; (c) Neon (Ne) has 8 valence electrons, 2 core electrons, and 0 unpaired electrons.

Step-by-step solution

Finding the atomic number of each element

The atomic number of an element determines the number of protons and electrons in a neutral atom of that element. Refer to table - 5.4 of your course textbook or any other reliable source like a periodic table to find the atomic numbers. - Carbon (C): Atomic number 6 - Phosphorus (P): Atomic number 15 - Neon (Ne): Atomic number 10

Writing the electron configurations

Using the atomic numbers, we will now determine the electron configurations for each of these elements. Remember the Aufbau principle, Pauli exclusion principle, and Hund's rule when filling the orbitals. Carbon (C): Atomic number = 6, thus 6 electrons in the configuration. Electron configuration: 1s^2 2s^2 2p^2 Phosphorus (P): Atomic number = 15, thus 15 electrons in the configuration. Electron configuration: 1s^2 2s^2 2p^6 3s^2 3p^3 Neon (Ne): Atomic number = 10, thus 10 electrons in the configuration. Electron configuration: 1s^2 2s^2 2p^6

Determining the valence electrons and core electrons

Valence electrons are those electrons that are present in the atom's outermost shell. Core electrons are those electrons that are in the atoms' inner shells. Carbon (C): Valence electrons: 2s^2 2p^2 = 4 valence electrons Core electrons: 1s^2 = 2 core electrons Phosphorus (P): Valence electrons: 3s^2 3p^3 = 5 valence electrons Core electrons: 1s^2 2s^2 2p^6 = 10 core electrons Neon (Ne): Valence electrons: 2s^2 2p^6 = 8 valence electrons Core electrons: 1s^2 = 2 core electrons

Finding the number of unpaired electrons

Unpaired electrons are electrons that occupy an orbital singly, not as part of an electron pair. We will find the number of unpaired electrons by looking at the electron configurations. Carbon (C): 2 unpaired electrons (2p orbital has 2 single electrons) Phosphorus (P): 3 unpaired electrons (3p orbital has 3 single electrons) Neon (Ne): 0 unpaired electrons (All orbitals are filled)

Results

- Carbon (C): 4 valence electrons, 2 core electrons, 2 unpaired electrons - Phosphorus (P): 5 valence electrons, 10 core electrons, 3 unpaired electrons - Neon (Ne): 8 valence electrons, 2 core electrons, 0 unpaired electrons

Key concepts

Atomic Structure

Atoms are the fundamental units of matter and have a complex internal structure. At the center is the nucleus, containing positively charged protons and neutral neutrons. Surrounding the nucleus are negatively charged electrons, which occupy various energy levels or shells. These electrons are bound to the atom by electromagnetic forces and are crucial in chemical bonding and the element's properties.

The arrangement and behavior of these particles give an element its unique characteristics. The number of protons in the nucleus determines the atomic number, which is unique to each element. This atomic number also reveals the number of electrons in a neutral atom. Electrons are arranged in orbitals within energy levels based on three main principles: the Aufbau principle, Pauli exclusion principle, and Hund's rule. Each principle guides how electrons fill available space around the nucleus, influencing how atoms interact with one another.

Valence Electrons

Valence electrons are the electrons located in the outermost energy level, or shell, of an atom. They play a pivotal role in chemical interactions because they are the electrons involved in forming bonds with other atoms.

In general, elements prefer to have a full set of valence electrons, often following the "octet rule," which suggests that atoms are most stable with eight valence electrons. However, some elements like hydrogen and helium are stable with two. For example, in carbon, which has an electron configuration of 1s\(^2\) 2s\(^2\) 2p\(^2\), the four valence electrons are in the second energy level (2s\(^2\) 2p\(^2\)). This configuration makes carbon versatile in forming different kinds of bonds.

Core Electrons

Core electrons are those that are not involved in chemical bonding and reside in the inner shells of an atom. These electrons form a "shield" that reduces the effective nuclear charge experienced by valence electrons.

Understanding the distinction between core and valence electrons is critical since core electrons do not typically participate in chemical reactions. For instance, neon, with an electron configuration of 1s\(^2\) 2s\(^2\) 2p\(^6\), has two core electrons (1s\(^2\)) and eight valence electrons (2s\(^2\) 2p\(^6\)). The filled valence shell makes neon chemically inert.

Unpaired Electrons

Unpaired electrons are single electrons found in an atom's orbitals that are not paired with another electron. They are significant because they determine an atom's magnetic properties and reactivity.

Unpaired electrons can cause the atom to form chemical bonds readily, often resulting in paramagnetism, where the atom is attracted to a magnetic field. For example, phosphorus has three unpaired electrons in its 3p orbital (3p\(^3\)) according to its electron configuration, which makes it reactive and able to form multiple bonds. On the other hand, elements like neon, with no unpaired electrons, are known for their stability and low reactivity.