Question

What is the ratio of the maximum possible number of \(f\) electrons to the maximum possible number of \(p\) electrons? 1\. \(\quad 2: 1\) 2\. \(4: 1\) 3\. \(7: 3\) 4\. \(15: 6\)

Short answer

The ratio of the maximum possible number of f electrons to the maximum possible number of p electrons is \(\boxed{7:3}\).

Step-by-step solution

Recall maximum electrons for f and p subshells

In an atom, the maximum number of electrons in a subshell depends on the value of the azimuthal quantum number (also known as the angular momentum quantum number) 'l'. The f subshell has an l value of 3, and the p subshell has an l value of 1. The maximum number of electrons in a subshell can be calculated using the formula: Maximum electrons = 2(2l + 1)

Calculate maximum f electrons

Using this formula and the l value for the f subshell (3), we can calculate the maximum possible number of f electrons: Maximum f electrons = 2(2 * 3 + 1) = 2(7) = 14

Calculate maximum p electrons

Now, using the formula and the l value for the p subshell (1), we can calculate the maximum possible number of p electrons: Maximum p electrons = 2(2 * 1 + 1) = 2(3) = 6

Determine the ratio

We have found that the maximum number of f electrons is 14 and the maximum number of p electrons is 6. Thus, the ratio of f electrons to p electrons is: Ratio (f:p) = 14:6 = 7:3 The correct answer is option 3: \(\boxed{7:3}\).

Key concepts

Azimuthal Quantum Number

The azimuthal quantum number, designated as 'l', plays a pivotal role in determining the shape of an electron's orbit within atoms and, by extension, the atomic structure. It is integral to the quantum mechanical model of the atom.

Every electron in an atom is described by four quantum numbers, and the azimuthal quantum number is the second. It can take on integer values from 0 to (n-1), where 'n' is the principal quantum number. For example, when 'l' equals 0, the orbitals are called 's' orbitals; for 'l' equals 1, they are 'p' orbitals; 'l' equals 2 designates 'd' orbitals; and 'l' equals 3 represents 'f' orbitals.

The azimuthal quantum number is intimately connected to the orbital angular momentum of the electron, and this directly impacts the chemical properties of the atom, such as bond formation and the atom's magnetic properties. Understanding the value of 'l' is key to identifying the specific subshells and the succinct characteristics of electrons within atoms.

Electron Subshell Capacity

The term 'electron subshell capacity' refers to the maximum number of electrons that a subshell can hold. This capacity is determined by the azimuthal quantum number 'l' and is given by the formula 2(2l + 1).

Each subshell type has a different capacity based on its 'l' value. For instance, the 's' subshell (l = 0) can hold a maximum of 2 electrons, 'p' subshell (l = 1) can hold up to 6 electrons, 'd' subshell (l = 2) can hold up to 10 electrons, and 'f' subshell (l = 3) can hold up to 14 electrons. Understanding this capacity is vital for determining how electrons are distributed in an atom and thus is crucial for predicting the atom's chemical behavior and reactivity.

With a firm grasp on electron subshell capacity, students will be more adept at envisioning electron configurations and exploring the intricacies of periodic properties such as atomic size, ionization energy, and electronegativity.

Atomic Structure

The concept of atomic structure is at the heart of chemistry and involves understanding how protons, neutrons, and electrons are arranged within an atom. Quantum numbers, including the azimuthal quantum number, play a significant role in determining an electron's position and energy within the atom.

Atoms possess a dense nucleus, housing protons with a positive charge, and neutrons with no charge, surrounded by a cloud of electrons with a negative charge. These electrons are found in specific regions called orbitals, and they obey the Pauli exclusion principle, which states that no two electrons can have all four quantum numbers in common.

The study of atomic structure also involves understanding electron configurations and the ordering of electrons in shells and subshells. This ordering is governed by the principles of quantum mechanics. Knowledge of atomic structure is fundamental in explaining periodic trends, the nature of chemical bonds, and the behavior of atoms during chemical reactions. By mastering the understanding of atomic structure, students can deepen their insight into the world on a microscopic scale, fueling the study of molecular interactions and the transformation of substances.