Modern Atomic Structure and Quantum Mechanics

A set of question-and-answer flashcards covering de Broglie’s matter waves, Heisenberg’s uncertainty principle, Schrödinger’s equation, and all four quantum numbers in the quantum-mechanical model of the atom.

Which two key developments led to the shift from Bohr’s model to the quantum-mechanical model of the atom?

(1) Dual behaviour of matter (wave–particle duality) and (2) Heisenberg’s uncertainty principle.

What dual property did de Broglie propose for all microscopic particles such as electrons?

They possess both particle-like and wave-like characteristics (wave–particle duality).

Write the de Broglie wavelength equation for a particle of mass m moving with velocity v.

λ = h / mv (or λ = h / p, where p is the linear momentum).

What name is given to the waves associated with material particles?

Matter waves or de Broglie waves.

Why is the de Broglie relationship mainly significant for microscopic bodies and not macroscopic ones?

For macroscopic objects the associated wavelength is extremely small, making wave behaviour imperceptible.

State Heisenberg’s uncertainty principle in words.

It is impossible to measure simultaneously and accurately both the position and the momentum of a microscopic particle.

Give the mathematical expression for Heisenberg’s uncertainty principle.

Δx · Δp ≥ h / 4π (or Δx · Δ(mv) ≥ h / 4π).

What crucial implication does the uncertainty principle have for electron paths in atoms?

It rules out the existence of well-defined circular (or fixed) orbits for electrons.

For which type of objects is the uncertainty principle most significant?

Microscopic objects (e.g., electrons) rather than macroscopic ones.

Define quantum mechanics.

The branch of science that describes the motion of microscopic objects while incorporating their wave–particle duality.

Who independently formulated quantum mechanics?

Werner Heisenberg and Erwin Schrödinger.

Write Schrödinger’s fundamental wave equation and name the operator H.

HΨ = EΨ, where H is the Hamiltonian (total-energy) operator.

What does the wave function Ψ represent, and what is the physical meaning of Ψ² ?

Ψ is a mathematical function of position; Ψ² gives the probability density of finding an electron in a region of space.

What is an atomic orbital?

A region in space around the nucleus where the probability of finding an electron is maximum.

List the four quantum numbers required to specify an electron and state what each describes in one phrase.

Principal (n) – main energy level; Azimuthal (l) – subshell/shape & angular momentum; Magnetic (ml) – orientation/individual orbital; Spin (ms) – spin orientation of the electron.

What information is conveyed by the principal quantum number n, and what symbols represent n = 1, 2, 3, 4 ?

It gives the shell, energy, and average distance from the nucleus; n = 1, 2, 3, 4 correspond to K, L, M, N shells respectively.

State the possible l values for a given principal quantum number n, and match l = 0, 1, 2, 3 with subshell labels.

l ranges from 0 to (n − 1); l = 0 → s, 1 → p, 2 → d, 3 → f.

What does the magnetic quantum number m_l determine and how many values can it take for each l?

It specifies orbital orientation; m_l can take (2l + 1) integral values from –l through 0 to +l.

Give the number of orbitals present in the s, p, d, and f subshells.

s: 1 orbital, p: 3 orbitals, d: 5 orbitals, f: 7 orbitals.

What values can the spin quantum number m_s assume, and what property does it describe?

m_s = +½ or –½; it describes the two possible spin orientations of an electron.