Question

Write a full set of possible quantum numbers for each of the following: (a) The outermost electron in an Rb atom (b) The electron gained when an \(\mathrm{S}^{-}\) ion becomes an \(\mathrm{S}^{2-}\) ion (c) The electron lost when an Ag atom ionizes (d) The electron gained when an \(\mathrm{F}^{-}\) ion forms from an \(\mathrm{F}\) atom

Short answer

a) n=5, l=0, m_l=0, m_s=\f+-1/2\; b) n=3, l=1, m_l=-1/0/1, m_s=\f+-1/2\; c) n=5, l=0, m_l=0, m_s=\f+-1/2\; d) n=2, l=1, m_l=-1/0/1, m_s=\f+-1/2\.

Step-by-step solution

- Identify the outermost electron's quantum numbers in an Rb atom

Rubidium (Rb) has an atomic number of 37. Its electron configuration is \( [Kr] 5s^1 \). The outermost electron is in the 5s orbital. The quantum numbers for this electron are: \( n = 5 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) or \( m_s = -\frac{1}{2} \).

- Determine the quantum numbers for the electron gained when S- ion becomes S2-

Sulfur (S) has an atomic number of 16. Its ground-state electron configuration is \( [Ne] 3s^2 3p^4 \). The extra electron makes the configuration \( [Ne] 3s^2 3p^5 \). The additional electron goes into the 3p orbital. The quantum numbers for this electron are: \( n = 3 \), \( l = 1 \), \( m_l = -1, 0, \text{or} \1 \), \( m_s = +\frac{1}{2} \) or \( m_s = -\frac{1}{2} \).

- Identify the quantum numbers for the electron lost when an Ag atom ionizes

Silver (Ag) has an atomic number of 47. Its electron configuration is \([[Kr] 4d^{10} 5s^1\) when neutral. The electron lost during ionization comes from the 5s orbital. The quantum numbers for this electron are: \( n = 5 \), \( l = 0 \), \( m_l = 0 \), \( m_s = +\frac{1}{2} \) or \( m_s = -\frac{1}{2} \).

- Determine the quantum numbers for the electron gained when an F- ion forms from an F atom

Fluorine (F) has an atomic number of 9. Its ground-state electron configuration for an F atom is \([He] 2s^2 2p^5\). When it gains one electron to become F-, the configuration becomes \([He] 2s^2 2p^6\). The extra electron enters the 2p orbital. The quantum numbers for this electron are: \( n = 2 \), \( l = 1 \), \( m_l = -1, 0, \text{or} \1 \), \( m_s = +\frac{1}{2} \) or \( m_s = -\frac{1}{2} \).

Key concepts

electron configuration

Electron configuration shows the distribution of electrons in an atom or ion.
The configuration specifies the orbitals that the electrons occupy around the nucleus.
For instance, the electron configuration for Rubidium (Rb) is \[\mathrm{[Kr] 5s^1}\].
This means Rb has the same core electronic structure as Krypton (Kr), plus one electron in the 5s orbital.
Understanding electron configurations can help us predict chemical properties and behaviors.
Each element on the periodic table has a unique electron configuration.
This configuration follows a set of rules called the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
The electron configuration can help us find the possible quantum numbers for electrons.
In the earlier exercise, these rules helped determine that for Rb, the outermost electron has quantum numbers: \[n = 5, l = 0, m_l = 0, m_s = +\frac{1}{2} \text{ or } -\frac{1}{2}\].

atomic orbitals

Atomic orbitals are regions around the nucleus where electrons are likely to be found.
They are described by quantum numbers which define their size, shape, and orientation.
The types of orbitals include s, p, d, and f.
For example, the outermost electron in Rb occupies a 5s orbital.
Orbitals can hold a maximum number of electrons based on the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.
An s orbital is spherical and can hold up to 2 electrons, while a p orbital has a dumbbell shape and can hold up to 6 electrons.
In the earlier exercise, when Sulfur (S) becomes \[\mathrm{S}^{2-}\], the extra electron enters a 3p orbital.
This orbital can have quantum numbers \[n = 3, l = 1, m_l = -1, 0, \text{ or } 1, m_s = +\frac{1}{2}\text{ or }-\frac{1}{2}\].
Knowing the orbital types helps to understand the electron locations in atoms and ions.

quantum mechanics

Quantum mechanics is the branch of physics that explains the behavior of particles at the atomic and subatomic levels.
This includes electrons within atoms.
The core idea is that particles like electrons have both particle and wave-like properties.
This duality is described by quantum numbers, which are solutions to the Schrödinger equation.
The four quantum numbers are: \ First, the principal quantum number (\(n\)) describes the energy level and size of the orbital.
\ Second, the angular momentum quantum number (\(l\)) describes the shape of the orbital.
\ Third, the magnetic quantum number (\(m_l\)) describes the orientation of the orbital.
\ Lastly, the spin quantum number (\(m_s\)) describes the direction of the electron's spin.
These quantum numbers help define the possible locations and behaviors of electrons in an atom.
In our exercise, identifying the quantum numbers for each electron involved using these principles.
For example, when an \(\mathrm{F}^-\) ion forms from an F atom, the extra electron's quantum numbers might be \[n = 2, l = 1, m_l = -1, 0, \text{or} 1, m_s = +\frac{1}{2} \text{or } -\frac{1}{2}\].
Quantum mechanics has broad implications in chemistry and physics, underlying our understanding of atomic structure and interactions.