Quantum Mechanical Model of the Atom

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Questions and Answers

What does Schrödinger's approach primarily utilize to specify any wavefunction?

Five quantum numbers
Four quantum numbers
Two quantum numbers
Three quantum numbers (correct)

Which of the following correctly identifies a type of quantum number used by Schrödinger?

z quantum number
n quantum number (correct)
x quantum number
p quantum number

The term 'zip codes for electrons' refers to which concept in quantum chemistry?

Chemical bonds
Atomic mass units
Electron shells
Quantum numbers (correct)

How many quantum numbers are used in Schrödinger’s approach to define an electron's state?

Three (C) Signup and view all the answers

Which of the following is NOT one of the three quantum numbers used in Schrödinger’s approach?

d quantum number (C) Signup and view all the answers

What values can the spin quantum number (s) take?

± ½ (B) Signup and view all the answers

Which statement is true regarding the angular momentum of particles?

It can be clockwise or anticlockwise, represented as (-1/2) and (+1/2). (D) Signup and view all the answers

What does the shape of the s-orbital depend on?

Only on R n,l (r). (A) Signup and view all the answers

Which of the following is a characteristic of the spin quantum number?

It describes the orientation of the electron spin. (A) Signup and view all the answers

In the context of s-orbitals, which statement is incorrect?

The value of R n,l (r) is irrelevant to the s-orbital's shape. (A) Signup and view all the answers

Flashcards

Spin quantum number (s)

The spin quantum number (s) describes the intrinsic angular momentum of an electron, which is also called spin angular momentum. It has two possible values: +1/2 and -1/2, representing spin up and spin down respectively.

Shape of s-orbital

S-orbitals have a spherical shape, which means the probability of finding an electron is the same in all directions at a given distance from the nucleus.

Quantum Numbers

A set of numbers that describe an electron's state in an atom.

Schrödinger's Equation

A mathematical equation that describes the behavior of electrons in atoms.

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Principal Quantum Number (n)

The principal quantum number, 'n', describes the electron's energy level.

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Angular Momentum Quantum Number (l)

The angular momentum quantum number, 'l', describes the shape of the electron's orbital.

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Magnetic Quantum Number (ml)

The magnetic quantum number, 'ml', describes the orientation of the electron's orbital in space.

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Study Notes

Lecture 05: Quantum Mechanical Model of the Atom

The quantum mechanical model of the atom treats electrons as matter waves.
Schrödinger proposed the quantum mechanical model.
The model describes the propagation of the wave associated with the particle.
The wave function (Ψ) describes the probability distribution of an electron's location.
The Hamiltonian operator (H) represents the total energy of the electron (kinetic energy + potential energy).
The eigenfunction (E) represents the energy levels that an electron can occupy.
The Schrödinger equation (ΗΨ = EΨ) describes the behavior of the electron in an atom.

Lecture 05: Wave Function of Hydrogen Atom

Wave function (ψ) in hydrogen atom is expressed as ψ(r, θ, φ) = R(r)Y(θ, φ).
R(r) is Radial wave function, which describes the distance from the nucleus.
Y(θ, φ) is Angular wave function, which defines the shape of the orbital.
ψ² is the probability of finding an electron at a certain location.

Lecture 05: Quantum Numbers

The quantum numbers describe the properties of atomic orbitals and electrons.
Principal quantum number (n): determines the main energy level (shell) and energy of electron. Values are positive integers (n = 1, 2, 3...).
n=1, 2, 3...
Maximum number of electrons in a shell = 2n2
Subsidiary (azimuthal) quantum number (ℓ) : determines the subshells (orbitals) within a shell.
ℓ = 0, 1, 2, 3 (s, p, d, f)
Magnetic quantum number (m_ℓ) : defines the orientation of the orbitals in space. Values range from -ℓ to +ℓ. m_ℓ = -ℓ, -ℓ+1, ..., 0, ..., ℓ-1, ℓ.
Spin quantum number (m_s) : describes the spin of the electron which can be either +1/2 or -1/2.

Lecture 06: Relative Energies of Orbitals and Building up Electronic Configurations

The lower the value of (n), the lower the energy of the orbital.
The lower the value of (n+l), the lower the energy of the orbital.
The order of orbital filling (Aufbau Principle) follows a specific path based on energy levels (such as 1s, 2s, 2p, 3s, 3p, 4s, 3d...).
Aufbau principle: Fill orbitals from lowest energy first.
Pauli Exclusion principle: No two electrons can have the same four quantum numbers.
Hund's rule: Within a subshell, each orbital occupies one electron before pairing.

Lecture 06: Electron Configurations for Elements and Ions

Electron configurations describe the arrangement of electrons in an atom's orbitals.
Elements configurations follow the Aufbau principle, Pauli exclusion principle, and Hund's rule.
The configuration of an ion differs from the neutral atom configuration by the number of electrons in the outermost orbitals.
Anomalous electronic configurations represent some exceptions to the Aufbau principle, particularly for transition metals.
Valence electrons are the outer shell electrons involved in chemical bonding, and core electrons are the inner shell electrons.
Noble gas configuration is a shorthand notation of core electrons.