Question

An ion having a \(4+\) charge and a mass of \(49.9\) amu has 2 electrons with principal quantum number \(n=1,8\) electrons with \(n=2\), and 10 electrons with \(n=3\). Supply as many of the properties for the ion as possible from the information given. (Hint: In forming ions for this species, the \(4 s\) electrons are lost before the \(3 d\) electrons.) a. the atomic number b. total number of \(s\) electrons c. total number of \(p\) electrons d. total number of \(d\) electrons e. the number of neutrons in the nucleus f. the ground-state electron configuration of the neutral atom

Short answer

In summary, the properties for the ion are: a. The atomic number: 24 b. Total number of s electrons: 6 c. Total number of p electrons: 12 d. Total number of d electrons: 2 e. The number of neutrons in the nucleus: ≈ 26 f. The ground-state electron configuration of the neutral atom: [Ar] 3d^2 4s^2

Step-by-step solution

Determine the atomic number (Z) and total number of electrons

Given that the ion has a 4+ charge, this means that it has lost 4 electrons. Therefore, the total number of electrons in the neutral atom would be: Total electrons = 2 (n=1) + 8 (n=2) + 10 (n=3) + 4 Total electrons = 24 Thus, the atomic number (Z) is 24.

Find the total number of s, p, and d electrons

The hint in the exercise tells us that in forming ions for this species, the 4s electrons are lost before the 3d electrons. So with the 4+ charge, we know that there are no 4s electrons left. We can now break down the electrons for each principal quantum number into their respective orbitals: n = 1: 1s^2 n = 2: 2s^2 2p^6 (since there are 8 electrons in n = 2) n = 3: 3s^2 3p^6 3d^2 (since there are 10 electrons in n = 3) Total s electrons = 2 + 2 + 2 = 6 Total p electrons = 6 + 6 = 12 Total d electrons = 2

Calculate the number of neutrons in the nucleus

The mass of the ion is given as 49.9 amu. The number of neutrons in the nucleus can be found by subtracting the atomic number (Z) from the mass: Number of neutrons = Mass - Atomic number Number of neutrons = 49.9 - 24 Number of neutrons ≈ 26 (rounded to nearest integer)

Determine the ground-state electron configuration of the neutral atom

Now that we know the number of electrons in each type of orbital, we can write the ground-state electron configuration of the neutral atom: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2 4s^2 The ground-state electron configuration of the neutral atom is [Ar] 3d^2 4s^2.

Key concepts

Atomic Number

The atomic number, often symbolized as 'Z', is a fundamental property of an element that indicates the number of protons present in the nucleus of an atom. Every atom of the same element shares the same atomic number, which is crucial because it essentially defines the element. For instance, the atomic number of oxygen is 8, meaning every oxygen atom has 8 protons. In our exercise, determining the atomic number was crucial to understand additional properties of the ion.

The atomic number also tells us about the number of electrons in a neutral atom. In the case of ions, you adjust for the charge to find the total number of electrons the ion gained or lost. Our example had a 4+ charge, indicating a loss of 4 electrons. By knowing the configuration of electrons at different energy levels, we could ascertain the neutral atomic number to be 24. Aside from defining the element, the atomic number also influences the chemical properties of an atom, including its electronegativity, ionization energy, and its place in the periodic table.

Electron Configuration

Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. Understanding electron configuration is pivotal for predicting how atoms interact to form chemical bonds. In our exercise, we looked closely at electron configuration to figure out the behavior of an ion with a particular charge. By considering the principal quantum numbers, we are able to break down the electrons into their respective orbitals like 1s, 2s, 2p, 3s, 3p, and 3d.

It's vital to remember the 'Aufbau principle', which states that electrons fill up the lowest energy orbitals first. Also, 'Hund's rule' tells us that electrons will fill up orbitals singly before pairing up. These principles help us determine the electron configuration for an element. For instance, the ground-state electron configuration we deduced for our neutral atom with the atomic number 24 is [Ar] 3d^2 4s^2, showing that after Argon's stable configuration, the next two electrons go into the 3d subshell, and the last two into the 4s.

Principal Quantum Number

The principal quantum number, denoted as 'n', defines the energy level at which an electron resides in an atom. It can take on positive integer values (1, 2, 3,...) increasing with distance from the nucleus. For example, electrons in the first energy level have a principal quantum number of 1 (n=1), which is closest to the nucleus and thus at the lowest energy state. In the exercise, the principal quantum numbers n=1, n=2, and n=3 showed the distribution of electrons across the different energy levels for the ion. These values are the primary indicators used to sort electrons into their shells.

Understanding 'n' is crucial when figuring out electron configurations, as it helps explain the structure of the periodic table and the reactivity of elements. It also has a bearing on the maximum number of electrons that can be housed in a shell, determined by the formula 2n². Moreover, knowledge of the principal quantum number, along with other quantum numbers, defines the unique address for each electron in an atom, paving the way to a complete understanding of its chemical behavior.