Unit 1: Atoms - Quantum Mechanical Model and Electron Configurations

Flashcards covering the Quantum Mechanical Model of the Atom, Electron Probability Density, Quantum Numbers, Orbital Shapes, Nodes, Pauli's Exclusion Principle, Many-Electron Atoms, Shielding, and Electron Configurations.

What is a wavefunction (ψ) in the context of the Schrödinger equation?

A function of 3D-coordinates, ψ(r, q, f), obtained by solving the Schrödinger equation, which can be factored into a radial part, R(r), and an angular part, Y(q, f).

What do chemists call wavefunctions for single electrons?

Orbitals.

What is the fundamental equation for the quantum mechanical model of the atom?

The Schrödinger equation (H"ψ=Eψ or (T# + V")ψ=Eψ).

What is probability density in the context of electrons?

A measure of the probability of finding the electron with distance from the nucleus along a line (r).

How is an electron cloud depicted?

As an imaginary picture of the electron changing its position rapidly over time, where a greater density of dots indicates a higher probability.

What does the radial probability distribution represent?

The total probability density.

What is a probability contour in atomic visualization?

A shape that defines a volume around the nucleus where the electron is found 90% of the time.

What are the different ways an orbital can be represented?

As ψ, as ψ², as electron density (probability), as a boundary surface, or as a radial probability distribution.

How is the state of an electron in an atom specified?

By a set of four quantum numbers.

What is the principal quantum number (n) and what does it indicate?

A positive integer (1, 2, 3…) that indicates the energy level of the orbital.

What is the angular momentum quantum number (l) and what does it determine?

It determines the shape of the orbital, and its allowed values are integers from 0 to n-1.

What is the magnetic quantum number (ml) and what does it determine?

It determines the orientation of the orbital in space, with allowed integer values from -l to +l.

How is the total number of orbitals for a given principal energy level (n) calculated?

By n².

What 'l' value corresponds to an s orbital?

l = 0.

What 'l' value corresponds to a p orbital?

l = 1.

What 'l' value corresponds to a d orbital?

l = 2.

How are orbitals identified using notation?

nℓmℓ, where n is the principal quantum number, ℓ is represented by a letter (s, p, d, f), and mℓ specifies the orientation (though often implied by shape).

What do orbital shapes represent?

The volume in which there is a 90% probability of finding the electron.

How do you calculate the number of radial nodes in an orbital?

of radial nodes = n – l – 1.

How do you calculate the number of angular nodes in an orbital?

of angular nodes = l.

How do you calculate the total number of nodes in an orbital?

of total nodes = n – 1.

What is the spin quantum number (ms) and what does it describe?

It describes the intrinsic angular momentum (spin) of the electron, with allowed values of +1/2 or -1/2.

What property does the principal quantum number (n) describe?

Orbital energy (size).

What property does the angular momentum quantum number (l) describe?

Orbital shape.

What property does the magnetic quantum number (ml) describe?

Orbital orientation.

What does Pauli's Exclusion Principle state?

No two electrons in an atom can have all four quantum numbers alike, meaning each orbital can be occupied by a maximum of two electrons of opposing spin.

What is the maximum number of electrons an s subshell can hold?

2 electrons.

What is the maximum number of electrons a p subshell can hold?

6 electrons.

What is the maximum number of electrons a d subshell can hold?

10 electrons.

What is the maximum number of electrons an f subshell can hold?

14 electrons.

Why do many-electron atoms require approximations in the Schrödinger equation?

The presence of electron-electron repulsions causes the energy of the orbitals to vary in a complex way, making exact solutions difficult.

What effect does a higher nuclear charge have on orbital energy and stability in an atom?

It increases the attraction from the nucleus, lowering the orbital energy and making the system more stable.

What is electron shielding?

Inner electrons preventing outer electrons from experiencing the full nuclear attraction.

What is penetration in the context of electron orbitals?

How well the outer electrons are able to get close to the nucleus.

How does a greater nuclear charge affect orbital energy?

Lowers orbital energy.

How do electron-electron repulsions affect orbital energy?

Raise orbital energy.

How do shielded outer electrons affect orbital energy?

They have higher energy.

How do orbitals with good penetration affect orbital energy?

They have lower energy.

What is the effective nuclear charge (Zeff)?

The net nuclear charge an electron experiences, which is reduced from the actual nuclear charge (Z) due to shielding.

For orbitals in the same shell, what is the order of penetration and shielding from most to least?

s > p > d > f.

For orbitals in the same shell, what is the order of energy from lowest to highest?

s < p < d < f.

What do radial distribution graphs describe?

The distribution of orbitals and the probability of finding an electron at a certain distance from the nucleus.

What describes the arrangement of electrons in an atom?

Electron configurations.

What is the Aufbau principle?

Electrons are added successively into the lowest energy orbitals first.

What is Hund's rule?

When orbitals of equal energy are available, electrons are distributed to maximize unpaired spins.

Which elements are noted for having "anomalous" electron configurations due to the special stability of half-filled or completely filled 3d subshells?

Chromium (Cr) and Copper (Cu).

What observation can be made about elements in the same group on the periodic table regarding their electron configurations?

They have similar valence electron configurations.

For a given energy level (n), how many orbitals are present?

n².

For a given energy level (n), what is the maximum number of electrons it can hold?

2n².