Question

How many 4\(d\) electrons would be predicted in the ground state for the following elements? a. zirconium b. cadmium c. iridium d. iron

Short answer

In the ground state, the number of 4\(d\) electrons for the given elements are: a. Zirconium: 2 b. Cadmium: 10 c. Iridium: 10 d. Iron: 0

Step-by-step solution

Find the atomic number of each element

Using the periodic table, find the atomic number (number of protons) for each element. This atomic number is also equal to the number of electrons in the ground state of the elements to make them electrically neutral. a. zirconium (Zr) - 40 b. cadmium (Cd) - 48 c. iridium (Ir) - 77 d. iron (Fe) - 26

Write the electron configurations for each element

Write the electron configurations of these elements using the Aufbau principle and Pauli's exclusion principle. The electron configurations will help us identify the total number of 4d electrons in each element: a. Zirconium (Zr): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^2\] b. Cadmium (Cd): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2\] c. Iridium (Ir): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^7\] d. Iron (Fe): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6\]

Count the number of 4d electrons for each element

Using the obtained electron configurations, count the number of 4d electrons for each of these elements: a. Zirconium (Zr): 2 electrons in 4d orbital b. Cadmium (Cd): 10 electrons in 4d orbital c. Iridium (Ir): 10 electrons in 4d orbital d. Iron (Fe): 0 electrons in 4d orbital (no 4d electrons) So, in the ground state, the number of 4\(d\) electrons are: a. Zirconium: 2 b. Cadmium: 10 c. Iridium: 10 d. Iron: 0

Key concepts

Atomic Number

The atomic number of an element is fundamental in understanding its properties and behavior. It represents the number of protons in an atom's nucleus. This number is unique to each element and is used to identify it on the periodic table. The atomic number is also equal to the number of electrons in a neutral atom. Hence, it helps determine the electron configuration of the element in its ground state.

For instance:

• Zirconium (Zr) has an atomic number of 40, so it has 40 protons and electrons.
• Cadmium (Cd) has an atomic number of 48.
• Iridium (Ir) has an atomic number of 77.
• Iron (Fe) has an atomic number of 26.

Understanding the atomic number is crucial because it forms the basis for further concepts like electron configuration and determines how elements interact with each other by forming bonds.

Ground State

The ground state of an atom is its lowest energy state. At this state, electrons are arranged in the most stable manner possible, occupying the least amount of energy orbitals first. This configuration is significant because it dictates the chemical behavior of elements. The electrons in the ground state are not excited, meaning they haven't absorbed energy to move to a higher energy level.

In atoms:

• Electrons occupy orbitals starting from the lowest energy level possible.
• Ground state configurations help us predict the chemical properties and reactivity of an element.

Knowing the ground state is important for solving electron configuration problems, as it helps identify how electrons are distributed in various orbitals without additional energy applied.

Aufbau Principle

The Aufbau principle is a rule used to determine the electron configurations of atoms. According to this principle, electrons fill the lowest available energy orbitals before moving to higher energy levels. This helps in forming the most stable electron configuration in the ground state. The principle also provides a sequential order for filling orbitals, which reflects the increasing energy levels.
For example:

• Electrons will fill the 1s orbital first, then move to the 2s, and so on.
• It establishes the basis for writing electron configurations, such as 1s² 2s² 2p⁶.

It's vital to understand the Aufbau principle because it is the starting framework for predicting electron arrangements in atoms, which directly influence their chemical and physical properties.

Pauli Exclusion Principle

The Pauli exclusion principle is a crucial concept in quantum mechanics that applies to electron configurations. It states that no two electrons in the same atom can have identical sets of four quantum numbers. What this means is that each electron in an atom must be unique in terms of its position and spin in an orbital.

• It restricts each orbital to holding a maximum of two electrons, each with opposite spins.
• This principle ensures that electrons are distributed properly across orbitals.

This principle is fundamental to understanding electronic structures, influencing everything from atom stability to chemical bonding. By ensuring that each electron is in a unique state, the Pauli exclusion principle helps maintain the atom's integrity and dictates the rules for how atoms interact chemically.