September 8th - Chemistry -Atomic Orbitals: Wave Functions, Nodes, and Quantum Numbers

A set of practice flashcards covering wave functions, nodes, orbital shapes (s, p, d), boundary diagrams, quantum numbers, orientation, and bonding concepts based on the lecture notes.

What does the wave function psi represent in atomic orbitals, and how is probability obtained?

Psi is the wave function; the probability of finding the electron is given by psi^2 (the square of the wave function), which is nonnegative.

What is a node in a three-dimensional orbital, and how many nodes does an nS orbital have?

A node is a region where the probability of finding the electron is zero. An nS orbital has n−1 total nodes (radial nodes for s orbitals).

What special feature does the 2s orbital have that the 1s orbital does not?

The 2s orbital has a spherical (radial) node in the middle where psi = 0 and is larger in size than 1s.

What is the boundary sphere for the 1s orbital, and what probability does it enclose according to the notes?

A boundary sphere around the nucleus within which there is about a 90% (textbooks may use 95% or 99%) probability of finding the electron.

How does the size of the 2s orbital compare to the 1s orbital?

The 2s orbital is larger than the 1s orbital and contains a spherical node.

What is the nodal feature of a p orbital?

A p orbital has an angular (nodal) plane through the nucleus where the probability of finding the electron is zero.

What do the quantum numbers n, l, and ml represent, and what are their typical meanings?

n is the shell (principal quantum number); l is the subshell (0 for s, 1 for p, 2 for d); ml is the orientation value, ranging from −l to +l.

For a 3p orbital, what are the possible ml values?

ml = −1, 0, +1 (with n = 3 and l = 1).

How many d orbitals are there, and what are their standard names?

Five d orbitals: dxy, dxz, dyz, dx^2−y^2, and d_z^2.

What are the three main features to consider when drawing atomic orbitals?

Shape, size, and orientation (and the phase across nodes).

How does phase relate to bonding interaction when two atomic orbitals overlap?

If the overlapping waves have the same phase, they form a bonding interaction; if the phases are opposite, the interaction is antibonding.

Why are s orbitals described as spherically symmetric in electron density?

Because their shape is a sphere around the nucleus, with density highest near the nucleus and decreasing with distance in all directions.

How does orbital size change with increasing principal quantum number n?

Orbital size increases with higher n; for example, 2s is larger than 1s, and 3s is larger than 2s.

How are p orbitals oriented in space, and how are they labeled relative to axes?

P orbitals are oriented perpendicular to each other and align with the x, y, and z axes (px, py, p_z); the specific labeling depends on the axis chosen in a drawing.

What is the relationship between s and p/d orbital sizes within the same shell, as discussed in the notes?

Within the same shell, orbitals can be similar in size (e.g., 2s and 2p are similar in size), and overall size increases with increasing n.