CHM 2103 (Wave Function, Orbitals, Schrödinger)

What is wave-particle duality?

The concept that electrons behave both as particles and as waves.

What is a wave function (ψ)?

A mathematical function that describes the behavior of an electron wave in space.

What does ψ² represent?

The probability density of finding an electron at a certain point in space.

What is an atomic orbital?

A region in space where there is a high probability of finding an electron.

What equation is used to describe the wave behavior of electrons?

The Schrödinger wave equation.

What type of system can the Schrödinger equation be solved exactly for?

A hydrogen-like system (one nucleus, one electron).

What coordinates describe electron position in Schrödinger's equation?

x, y, and z coordinates (Cartesian system), or spherical polar coordinates.

What is the simplified form of Schrödinger's equation in 1D?

d²ψ/dx² + (8π²m/h²)(E-V)ψ = 0

What does solving the Schrödinger equation yield?

Allowed energy values (E) and wave functions (ψ).

Why is ψ² more important than ψ?

ψ² has physical meaning — it gives the probability of finding an electron.

What are the required properties of a valid wave function ψ?

It must be finite, single-valued, and continuous in all directions.

What are the two parts of a wave function ψ?

Radial part (R(r)) and angular part (A(θ,φ)).

What determines the shape of atomic orbitals?

The angular part of the wave function (A(θ,φ)).

What shape does an s orbital have?

Spherical.

What shape does a p orbital have?

Dumbbell-shaped.

What shape does a d orbital have?

Four-lobed (cloverleaf-shaped).

How were the shapes of orbitals determined?

By solving the Schrödinger equation and plotting ψ² as contour plots.

What are quantum numbers used for?

To describe the unique properties of atomic orbitals.

What is the principal quantum number (n)?

A positive integer (1 ≤ n ≤ ∞) that determines the energy level and size of the orbital.

What is the orbital/azimuthal quantum number (l)?

A quantum number (0 to n-1) that determines the shape of the orbital.

What are the values of l for s, p, d, and f orbitals?

s: l=0, p: l=1, d: l=2, f: l=3.

What is the magnetic quantum number (ml)?

A quantum number that determines the orientation of the orbital; values range from -l to +l.

What is the spin quantum number (ms)?

A quantum number with values of +½ or -½; represents electron spin.

What is a degenerate orbital?

An orbital with the same energy level as others of the same type and n value.

How many s orbitals exist for a given value of n?

Only one (singly degenerate, ml = 0).

How many p orbitals exist when n ≥ 2?

Three (triply degenerate: ml = -1, 0, +1).

How many d orbitals exist when n ≥ 3?

Five (five-fold degenerate: ml = -2, -1, 0, +1, +2).

How many f orbitals exist when n ≥ 4?

Seven (seven-fold degenerate: ml = -3 to +3).

What is the maximum number of electrons each orbital type can hold?

s = 2, p = 6, d = 10, f = 14

How is an atomic shell different from an atomic orbital?

A shell is a group of orbitals with the same n value; orbitals are subsets of shells.

What letters represent electron shells?

K, L, M, N (corresponding to n = 1, 2, 3, 4).

What do the terms 1s, 2p, 3d, etc. represent?

Specific orbitals, labeled by principal (n) and azimuthal (l) quantum numbers.

Why are orbitals labeled as 1s, 2s, 2p, 3s, 3p, 3d, etc.?

To show both their energy level (n) and shape type (s, p, d, etc.).

What does the Schrödinger equation show about quantized states?

It naturally leads to the quantization of energy levels in atoms.

How many electrons can occupy one atomic orbital?

A maximum of two electrons.

What does the Schrödinger equation describe for an electron?

Its allowed energy levels and spatial behavior inside an atom.

What is the significance of ψ² contour plots?

They reveal the shape and structure of atomic orbitals.