September 10th Wednesday -Quantum Orbitals and Quantum Numbers (Bohr-De Broglie-Schrödinger)

Flashcards covering Bohr and De Broglie ideas, Schrödinger equation, orbitals, and quantum numbers (n, l, m_l) including s, p, and d orbitals.

According to the notes, how are the electron’s allowed orbits in a hydrogen atom constrained by the Bohr model?

The angular momentum is quantized so the circumference of the orbit equals an integer number of de Broglie wavelengths (nλ).

What did De Broglie propose about particles like electrons and their relation to waves?

Particles can behave as waves; matter waves exist, and electrons can form standing waves around the nucleus with wavelengths related to their momentum.

How do the orbits described by De Broglie differ from classical orbits around the nucleus?

They are standing waves around the nucleus, not classical circular paths; exact position and momentum cannot be specified simultaneously.

What fundamental principle relates position and momentum uncertainty in these notes?

The more precisely the position is known, the less precisely momentum is known, and vice versa.

What are virtual particles and what is their significance mentioned in the notes?

Particles that can appear and disappear briefly due to quantum fluctuations and can have real effects despite being transient.

What do the solutions of the Schrödinger equation represent?

They give orbitals or wavefunctions that describe the probability of finding the electron.

What is the analogy used to explain how quantum numbers define an electron’s location (address) in an atom?

A quantum-number set serves as an address: n (shell), l (shape), and m_l (orientation).

What does the principal quantum number n indicate?

The shell or energy level; it defines the size of the orbital for hydrogen-like atoms.

What does the angular momentum quantum number l indicate, and what are its allowed values for a given n?

l defines the orbital shape; allowed values range from 0 to n-1 (0,1,2,…).

Which orbital labels correspond to l = 0, l = 1, and l = 2?

l = 0 → s; l = 1 → p; l = 2 → d.

For n = 1, what is the possible l value and orbital label?

l = 0, corresponding to the 1s orbital.

For n = 2, what are the possible l values and corresponding orbitals?

l = 0 (2s) and l = 1 (2p).

How many p orbitals exist in a shell, and what are they commonly named?

Three p orbitals (px, py, p_z) with the same energy.

What are the possible magnetic quantum numbers m_l for l = 1 (p orbitals)?

m_l = -1, 0, +1.

What happens when n = 3 in terms of allowable l values and orbital types?

l can be 0, 1, or 2, corresponding to 3s, 3p, and 3d orbitals.

How are the shapes of s, p, and d orbitals described?

s is spherical; p orbitals are dumbbell-shaped along axes; d orbitals have more complex lobed shapes.

How many d orbitals exist and what are their m_l values?

Five d orbitals with m_l values -2, -1, 0, +1, +2.

Why are there multiple p orbitals for a given shell, and how are they labeled?

Because p orbitals have three spatial orientations (px, py, p_z); they are degenerate in energy.

What is the physical meaning of an orbital’s phase in the context of lobes?

Different lobes can have different phases; the phase difference affects interference, while probability density comes from the square of the wavefunction.

What does degeneracy mean in the context of orbitals within a shell?

Orbitals with the same energy (e.g., the three 2p orbitals) are degenerate.

What is the Cartesian-axis labeling of the three p orbitals as described in the notes?

px along the x-axis, py along the y-axis, p_z along the z-axis.

What is the complete set of quantum numbers used to describe an electron in an orbital, as discussed in the notes?

n, l, and m_l (with spin being an additional quantum number not detailed here).