Question

Indicate the number of unpaired electrons present in each of the following atoms: \(\mathrm{B}, \mathrm{Ne}, \mathrm{P}, \mathrm{Sc}, \mathrm{Mn}, \mathrm{Se}, \mathrm{Kr}\) \(\mathrm{Fe}, \mathrm{Cd}, \mathrm{I}, \mathrm{Pb}\).

Short answer

B: 1, Ne: 0, P: 3, Sc: 1, Mn: 5, Se: 2, Kr: 0, Fe: 4, Cd: 0, I: 1, Pb: 2.

Step-by-step solution

Write Electron Configurations

Start by writing the electron configuration for each element. This will help determine the number of unpaired electrons. For example: \(\mathrm{B} = 1s^2 2s^2 2p^1\), \(\mathrm{Ne} = 1s^2 2s^2 2p^6\), \(\mathrm{P} = 1s^2 2s^2 2p^6 3s^2 3p^3\), \(\mathrm{Sc} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^1 4s^2\), \(\mathrm{Mn} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^2\), \(\mathrm{Se} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^4\), \(\mathrm{Kr} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6\), \(\mathrm{Fe} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2\), \(\mathrm{Cd} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2\), \(\mathrm{I} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^5\), \(\mathrm{Pb} = 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 4f^{14} 5d^{10} 6s^2 6p^2\).

Identify Unpaired Electrons

Examine the electron configurations, focusing on the outermost subshells, especially the \(p\) and \(d\) subshells. Count the number of electrons in each subshell and identify how many are unpaired. Examples: For \(\mathrm{B}\), there is 1 unpaired electron in \(2p^1\). For \(\mathrm{Ne}\), there are 0 unpaired electrons in \(2p^6\). Continue for each element.

Key concepts

Electron Configuration

Electron configurations are like a map of where electrons reside in an atomic structure. Visualizing an atom, imagine a small nucleus surrounded by cloud layers that are regions where electrons are likely to be found. These layers are more formally known as orbitals. Orbitals are grouped into energy levels or shells, and each has a different capacity for holding electrons:

• The first shell can hold up to 2 electrons.
• The second shell can hold up to 8 electrons.
• The third and further shells can hold even more.

Each of these shells contains subshells, labeled as s, p, d, and f. When writing an element's electron configuration, numbers indicate the energy level, and letters (s, p, d, f) indicate the type of orbital. For instance, the electron configuration for Boron is presented as: \(1s^2 2s^2 2p^1\). Here:

• "1s" indicates the first energy level with s orbital full (2 electrons).
• "2s" indicates the second energy level with s orbital also full (2 electrons).
• "2p" has one electron, meaning there’s one unpaired electron at this level.

By understanding this kind of notation, you can predict properties such as magnetism and reactivity.

Chemical Elements

Chemical elements make up all matter and each element has a unique number of protons, which determines its place on the periodic table. Every element is represented by a symbol, like H for hydrogen or Fe for iron. Elements can be sorted based on several factors such as:

• Atomic number: This is simply the number of protons in the nucleus.
• Atomic mass: This takes into account the mass of protons and neutrons inside the nucleus.
• Groups/Families: Columns in the periodic table where elements share similar properties. For example, the noble gases, like neon (Ne) and krypton (Kr), are in a column known for being colorless, odorless, and largely non-reactive.
• Periods: Rows in the periodic table where elements have the same number of atomic orbitals.

Every chemical element interacts and bonds with others in different ways, forming the variety of substances that we see around us. Understanding these basics helps in predicting how elements will behave, especially when unpaired electrons are involved.

Quantum Mechanics

Quantum mechanics is the branch of physics that deals with the behavior of very small particles, namely electrons, within an atom. The strange and fascinating world of quantum mechanics helps to explain how electrons move and occupy orbitals. Some of its key principles include:

• Quantization of energy levels: Electrons in an atom can only exist in specific energy levels, not between them. This quantization is crucial to understanding electron configurations.
• Wave-particle duality: Electrons exhibit properties of both waves and particles. This dual nature is important when predicting electron positions in their orbitals.
• Uncertainty Principle: Part of quantum mechanics is that we can't know both the position and the momentum of an electron with absolute certainty. This principle illustrates the probabilistic nature of electron positions.

Quantum mechanics offers insights into why electrons fill orbitals in certain ways, helping us to predict phenomena like the presence of unpaired electrons.

Atomic Structure

The atomic structure is the organization of electrons around the nucleus of an atom. It's a fundamental concept that influences how atoms interact.Key points in atomic structure include:

• Nucleus: At the heart of an atom, it contains protons and neutrons, accounting for most of an atom's mass.
• Electrons: Negatively charged particles that orbit the nucleus in regions defined by their energies, known as orbitals.
• Shells and Subshells: Electrons move in shells (energy levels) around the nucleus. These are further divided into subshells (s, p, d, f) where electrons reside based on their energy.

Understanding atomic structure allows us to comprehend electron arrangements and predict their behavior in chemical reactions. For instance, an element like manganese (Mn) with its configuration \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^2\) has unpaired electrons in the d subshell, impacting its magnetic properties and reactivity.