Quantum Orbitals and Wave Functions - Lecture Review

A set of practice questions (flashcards) covering wave functions, probability, nodes, orbital shapes (s, p, d), quantum numbers, boundary diagrams, and phase considerations from the lecture notes.

What does the wave function psi (or the Schrödinger wave function) describe in atomic orbitals?

It describes the state of the electron and depends on distance from the nucleus; psi^2 gives the probability density of finding the electron.

How is the probability of finding an electron at a point related to psi?

Probability density is psi^2, which is non-negative.

For the 1s orbital, how does the probability of finding the electron change as you approach the nucleus?

The probability increases; there is a higher electron density near the nucleus.

What feature appears in the 2s orbital that is not present in the 1s orbital?

A spherical node (a region where the probability is zero) where psi changes sign.

What is a node in a three-dimensional atomic orbital?

A region (plane or surface) where the probability of finding the electron is zero.

What is the relationship between the number of nodes and the principal quantum number n?

The total number of nodes equals n − 1 (e.g., 2s has 1 node, 3s has 2 nodes).

How many p orbitals exist in a given shell and what are their orientations?

There are three p orbitals corresponding to ml = −1, 0, +1, typically oriented as px, py, p_z.

Do the ml values uniquely assign a spatial direction for p orbitals?

No; ml values label the degeneracy, but orientation (x, y, z) depends on the chosen axes.

How many d orbitals are in a shell and what is their general shape?

Five d orbitals; shapes include four-lobed forms and others with donut-like or more complex lobes, often with nodal planes.

Give examples of common d-orbital names and their general shapes.

Examples include dxy, dyz, dxz (four lobes), dx^2−y^2 (lobes along x and y), and d_z^2 (donut around z with axial lobes).

What are the quantum numbers n, l, and m_l?

n is the shell, l is the subshell (0=s, 1=p, 2=d, etc.), and m_l is the magnetic quantum number describing orientation (values from −l to +l).

What is the boundary diagram for a 1s orbital and what does it signify?

A sphere around the nucleus representing the region containing about 90% (textbook-dependent) of the electron probability.

How does the size of orbitals change with increasing n (e.g., 1s vs 2s vs 3s?

Higher n means a larger orbital; 2s is larger than 1s, and 3s is larger than 2s.

What is a nodal plane in a 2p orbital?

A plane through the nucleus where the probability of finding the electron is zero (a nodal plane).

How is the concept of phase represented in three-dimensional orbital plots?

Phase is shown by color or shading; crossing a node involves a phase change (sign change) in the wave function.

Why is the phase important for molecular bonding (bonding vs antibonding)?

Same phase (constructive interference) leads to bonding; opposite phase (destructive interference) leads to antibonding.

What is the orientation naming for the p orbitals in Cartesian coordinates?

px, py, p_z are oriented along the x, y, and z axes respectively.

What is the significance of nodes when comparing s, p, and d orbitals?

Nodes indicate regions of zero probability; the number and type of nodes increase with the principal quantum number and orbital type (e.g., 1s has none, 2s has one radial node, 2p has a nodal plane).