Quantum Mechanics

What does the principal quantum number (n) represent?

The energy level/shell; size and energy of orbital (n = 1, 2, 3…).

What values can the angular momentum quantum number (ℓ) take?

A: ℓ ranges from 0 → (n − 1). It defines the orbital type (s=0, p=1, d=2, f=3).

Q: What does mℓ (magnetic quantum number) represent?

A: The orientation of the orbital; integer values from −ℓ to +ℓ.

Q: What are the possible values of the spin quantum number (ms)?

A: +½ or −½.

Q: How many orbitals are in a subshell with ℓ = 2?

A: 5 orbitals (d subshell).

Q: How many orbitals are in the n=4 shell?

A: n² = 16 orbitals.

Q: How many electrons can a single orbital hold?

A: 2 electrons with opposite spins.

Q: What principle states “no two electrons can have the same four quantum numbers”?

A: Pauli Exclusion Principle.

Q: What rule says orbitals fill singly first before pairing?

A: Hund’s Rule.

Q: What is the Aufbau principle?

A: Electrons fill orbitals in order of increasing energy (lowest first).

Q: Write the orbital designation for n=5, ℓ=2.

A: 5d.

Q: How many unpaired electrons does Fe³⁺ have?

A: 5 (3d⁵, half-filled).

Q: Which orbitals are filled first: 4s or 3d?

A: 4s fills first, but electrons are removed from 4s before 3d in cations.

Q: How many orbitals are in the p subshell?

A: 3 orbitals (mℓ = −1, 0, +1).

Q: What orbital type corresponds to ℓ = 3?

A: f orbital.

Q: What causes the “big jump” in successive ionization energies?

A: Removing core electrons after all valence electrons are gone.

Q: What is the electron configuration of Cr³⁺?

A: [Ar] 3d³.

Q: What is the maximum number of electrons in the n=3 shell?

A: 2n² = 18 electrons.

Q: Which has more unpaired electrons: N (2p³) or O (2p⁴)?

A: N (3 unpaired vs. O with 2 unpaired).