Electron Structure of Atoms: Atomic Orbitals - Lecture 4

These flashcards cover key concepts from the lecture on electron structure of atoms, including atomic orbitals, quantum numbers, Schrödinger's equation, nuclear shielding, electron spin, and the building-up principle.

What major topics are covered in the lecture on Electron Structure of Atoms: Atomic Orbitals?

Effective nuclear charge, electron configuration, and the periodic table are covered.

What does Schrödinger's equation allow one to compute for a hydrogen atom?

Schrödinger's equation enables one to compute the states of an electron in 1H, each consisting of a wave function (ψn) and its energy (En).

What do the chemical labels s, p, d, and f correspond to in relation to atomic orbitals?

These labels correspond to different values of the angular momentum quantum number (l).

What is an 'ansatz' in the context of solving equations, particularly Schrödinger's equation?

An ansatz is an assumption about the form of a function to help solve a given equation, originating from the German word meaning 'guess' or 'starting point'.

What defines an admissible radial orbital function R(r)?

An admissible radial orbital function R(r) is one that does not diverge, which implies the total energy E = −ℰ0/n^2, where n = l + 1, l + 2, and so on.

What is the definition of radial orbital functions Rnl(r) and the constraints on quantum numbers n and l?

Radial orbital functions Rnl(r) are admissible solutions of the radial equation where n and l are integer numbers such that 0 ≤ l < n, and ℰ0 = 13.60 eV is the atomic unit of energy.

What is the relationship between the number of nodes in a radial orbital function Rnl(r) and its quantum numbers n and l?

The number of nodes in Rnl(r) equals n - l - 1.

What are the three quantum numbers that describe an electron state in a hydrogen atom?

The three quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), and the magnetic quantum number (m).

How does the electron energy in a 1H atom depend on its quantum numbers?

The electron energy En depends only on the principal quantum number (n), given by En = −ℰ0/n^2.

What defines a hydrogen-like atom?

A hydrogen-like atom is a one-electron atom with a nuclear charge Z > 1, carrying a net charge of (Z-1)+.

How does increasing the nuclear charge Z affect the energy and size of an orbital in a hydrogen-like atom?

The energy of an electron in a hydrogen-like atom is proportional to Z^2 (En = Z^2ℰ0/n^2), meaning stronger attraction and lower (more negative) energy levels. The orbital is Z times smaller.

What is nuclear shielding, and how does it impact electron-nucleus attraction in many-electron atoms?

Nuclear shielding is the phenomenon where electron-electron repulsion causes the attraction of an electron to the nucleus to be weaker in a many-electron atom compared to a hydrogen-like atom.

What is the Stern-Gerlach effect, and what does it reveal about electrons?

The Stern-Gerlach effect is a phenomenon that demonstrates that the magnetic moment of an electron can only have two possible values ('up' and 'down'), revealing the electron spin.

Define electron spin.

Electron spin is the magnetic moment carried by the electron, a quantum property that can take only two possible values (±ψB) along an axis of measurement.

What are the three rules of the building-up principle (Aufbau principle) for determining the electron configuration of an atom?

The three rules are: (1) electrons fill orbitals starting from the lowest energy level (orbital energy minimization), (2) no more than two electrons (spin up and spin down) can occupy an orbital (Pauli's exclusion principle), and (3) if orbitals have the same energy, it is preferred to occupy separate orbitals with parallel spins rather than fewer orbitals with antiparallel spin (Hund's rule).

According to Pauli's exclusion principle, how many electrons can occupy a single atomic orbital and with what spin configuration?

No more than two electrons can occupy an orbital, and they must have opposite spins (spin up and spin down).

Why do elements in the same column of the periodic table often have similar chemical properties?

Elements in the same column share similar chemical properties because they typically have the same outermost electron (valence electron) configuration.