September 5th - Chemistry -Quantum Orbitals, De Broglie Waves, and Quantum Numbers (Lecture Notes)

Flashcards covering de Broglie waves, standing-wave quantization, uncertainty principle, Schrödinger equation, and quantum-number-based orbital descriptions (n, l, m_l; s, p, d orbitals).

What quantizes electron orbits according to the standing-wave view in hydrogen?

The circumference of the orbit must be an integer multiple of the electron's de Broglie wavelength, leading to quantized angular momentum.

What did de Broglie propose about particles such as electrons?

They can behave as waves and exhibit wave-like properties.

In this quantum view, how are electrons around the nucleus described?

As standing waves surrounding the nucleus rather than as classical circular orbits.

State the Heisenberg uncertainty principle as described in the notes.

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

What is the role of the Schrödinger equation in atomic physics?

It yields the wave functions (orbitals) and their corresponding probability distributions.

Why do we use a set of quantum numbers to describe orbitals?

To give each orbital a unique address defined by n, l, and m_l (and spin).

What does the principal quantum number n represent?

The energy shell or principal level; Bohr introduced it to describe shell structure.

What does the azimuthal (l) quantum number determine?

The orbital shape; l=0 for s, l=1 for p, l=2 for d.

What does the magnetic quantum number m_l indicate?

The orientation of the orbital in space; values range from -l to +l.

What is the quantum-number set for a 1s orbital?

n = 1, l = 0, m_l = 0.

What is the quantum-number set for a 2s orbital?

n = 2, l = 0, m_l = 0.

What is the quantum-number set for the 2p orbitals?

n = 2, l = 1, m_l ∈ { -1, 0, +1 }.

How many p orbitals exist for a given n, and what are their directions?

Three p orbitals (px, py, pz) corresponding to ml = -1, 0, +1 and oriented along x, y, z axes.

For n = 3, what are the possible l values and corresponding orbital types?

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

How many d orbitals are there and what are their magnetic quantum numbers?

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

What is the shape of the s orbital and the orientation of p orbitals?

The s orbital is spherical with no orientation; p orbitals have two lobes oriented along axes (px, py, p_z).