Question

In the modern theory of the atom, a(n) _______ resents a region of space in which there is a high probability of finding an electron.

Short answer

In the modern theory of the atom, a(n) \(\textbf{orbital}\) represents a region of space in which there is a high probability of finding an electron.

Step-by-step solution

Find the correct term

According to the modern theory of the atom, which is based on the quantum mechanical model, the term that represents a region of space in which there is a high probability of finding an electron is called an "orbital". An orbital is a mathematical function that describes the wave-like behavior of an electron around the nucleus of an atom. Different types of orbitals (s, p, d, and f orbitals) have different shapes and orientations, but they all represent areas where electrons are most likely to be found. Therefore, the correct term is "orbital". In the modern theory of the atom, an orbital represents a region of space in which there is a high probability of finding an electron.

Key concepts

Orbitals

In the realm of quantum mechanics, an 'orbital' is a fundamental concept when discussing the intricate behaviors of electrons within atoms. Unlike the outdated models that depicted electrons orbiting the nucleus in fixed paths, the quantum mechanical model introduces orbitals as mathematical functions that denote the likelihood of an electron's presence in a particular region around an atom's nucleus.

The shapes of these orbitals are determined by the quantum numbers associated with electrons, with each type of orbital (s, p, d, and f) showcasing unique geometries that define the spatial distribution of where an electron is likely to be found. For instance:

• The s orbital is spherical in shape, encompassing the nucleus,
• The p orbitals are dumbbell-shaped and orient in three-dimensional space along the x, y, and z axes,
• The d and f orbitals exhibit even more complex shapes and orientations, reflecting the increasing energy and angular momentum of electrons associated with these orbitals.

Understanding orbitals is crucial not just for envisioning where an electron might exist relative to the nucleus, but also for comprehending the chemical bonding and reactivity of elements.

Electron Probability

Diving deeper into the quantum mechanical model, 'electron probability' advances our comprehension of atomic behavior beyond mere orbits. This concept encapsulates the likelihood of finding an electron in a given space within the atomic cloud.

This probability is derived from the wave function - a mathematical description of the quantum state of a system. The square of the wave function's amplitude at any given point in space gives us the probability density for an electron's presence at that location. It is important to understand that:

• High electron probability areas are where electrons spend most of their time,
• These areas correlate directly with the orbitals mentioned earlier,
• Electron probability distribution aids in predicting electron configurations and chemical properties.

Role of Electron Probability in Bonding

Electron probability also plays a significant role in chemical bonding. In a covalent bond, for example, the electron probability distribution overlaps between two atoms, signaling a shared pair of electrons, and thus a bond formation.

Atomic Structure

Exploring the atomic structure through the lens of quantum mechanics offers a dramatic departure from classical imagery of atoms with neat planetary electron orbits. The modern quantum mechanical model introduces a layered structure to the atom which includes a dense nucleus surrounded by a cloud of electrons located in orbitals.

The nucleus resides at the center and contains protons and neutrons - collectively known as nucleons. Surrounding the nucleus, the electrons exist in cloud-like regions defined by their orbitals. Each electron is characterized by a set of quantum numbers which dictate its properties and the space it occupies around the nucleus. These include:

• The principal quantum number, indicating the electron's shell and relative size of the orbital,
• The angular momentum quantum number, determining the shape of the orbital,
• The magnetic quantum number, which tells the orientation of the orbital,
• The spin quantum number, representing the electron's inherent spin.

The organization of electrons into various orbitals within different energy levels is responsible for the periodic properties observed across elements. Thus, atomic structure is a multi-layered, intricate concept that reveals the complex interactions governing an atom's behavior and its interactions with other atoms.