Question

Determine the maximum number of electrons that can be found in each of the following subshells: \(3 s, 3 d, 4 p\), \(4 f, 5 f\).

Short answer

3s: 2 electrons, 3d: 10 electrons, 4p: 6 electrons, 4f: 14 electrons, 5f: 14 electrons.

Step-by-step solution

Understanding Electron Capacity per Orbital

The maximum number of electrons that can be found in a subshell depends on the number of orbitals in that subshell. Each orbital can hold a maximum of 2 electrons.

Determine the Number of Orbitals per Subshell

- The 's' subshell contains 1 orbital. - The 'p' subshell contains 3 orbitals. - The 'd' subshell contains 5 orbitals. - The 'f' subshell contains 7 orbitals.

Calculate Maximum Electrons for Each Subshell

- For the 3s subshell: 1 orbital x 2 electrons/orbital = 2 electrons. - For the 3d subshell: 5 orbitals x 2 electrons/orbital = 10 electrons. - For the 4p subshell: 3 orbitals x 2 electrons/orbital = 6 electrons. - For the 4f and 5f subshells: 7 orbitals x 2 electrons/orbital = 14 electrons each.

Key concepts

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. They are like the houses for electrons in an atom. Think of them as clouds where electrons hang out. Each atomic orbital is characterized by a particular shape and energy level.
These orbitals are defined by quantum numbers, which are a set of values that describe the energy, shape, size, and orientation of the orbital.

• The most common types of orbitals are represented by the letters s, p, d, and f.
• s orbitals are spherical.
• p orbitals are dumbbell-shaped.
• d and f orbitals have more complex shapes.

Atomic orbitals play a critical role in chemical bonding and determine how atoms interact with each other. Understanding their arrangements helps explain the structure of the periodic table and the properties of different elements.

Electron Capacity

Electron capacity refers to the maximum number of electrons that can occupy an atomic orbital or subshell. Each type of orbital has a specific electron capacity, which is determined by the number of available orbitals within the subshell.
Here’s a simple way to remember:

• The 's' subshell has 1 orbital, holding up to 2 electrons.
• The 'p' subshell has 3 orbitals, able to accommodate up to 6 electrons.
• The 'd' subshell contains 5 orbitals, with a capacity of 10 electrons.
• The 'f' subshell has 7 orbitals, supporting up to 14 electrons.

This simple pattern helps determine the electron arrangement or electron configuration of an atom, crucial for predicting the atom's chemical behavior and reactivity.

Subshells

Subshells are subdivisions of electron shells in an atom. They consist of a set of orbitals that share the same energy level but differ in their spatial orientation. Each shell in an atom is made up of one or more subshells.
Here’s how subshells break down:

• The first electron shell (n = 1) only has an 's' subshell.
• The second shell (n = 2) has 's' and 'p' subshells.
• The third shell (n = 3) includes 's', 'p', and 'd' subshells.
• The fourth and higher shells (n ≥ 4) contain 's', 'p', 'd', and 'f' subshells.

Subshells are significant because they dictate how atoms build up their electrons, impacting the atom's energy state, chemical properties, and how they interact with other atoms.

Quantum Mechanics

Quantum mechanics is the branch of physics that explains the behavior of atoms and electrons at the smallest scales. It provides the fundamental framework for understanding atomic orbitals, electron configurations, and how electrons move within those orbitals.
In quantum mechanics, electrons exhibit both particle-like and wave-like properties, which means:

• The exact location of an electron cannot be determined, only the probability of finding an electron in a specific region.
• Electrons fill orbitals in a way that minimizes the atom's energy, known as the Aufbau principle.
• Pauli's exclusion principle states that no two electrons in an atom can have the same set of quantum numbers.
• Hund's rule asserts that electrons will fill an unoccupied orbital before they pair up in an occupied one.

These principles are key for understanding how atoms form molecules, the nature of chemical bonds, and the diverse behavior of elements in the periodic table.