Atomic Structure and Quantum Mechanics

Planck's Theory

The energy emitted by radiation is directly proportional to the frequency of radiation.

Bohr Model

Postulates:

1. Electrons revolve around the nucleus in circular orbits without emitting energy.
2. Electrons are only allowed in orbits where their angular momentum is a multiple of h/2π.
3. When an electron moves between orbits, the energy difference is emitted as radiation.

Bohr determined the radius, energy, and location of electrons within these orbits.

Sommerfeld's Modifications

Sommerfeld modified the Bohr model to include elliptical orbits. He introduced a second quantum number, which depends on the first and describes the orbit's shape.

l = 0 ... (n-1)

Zeeman Effect: When an atomic spectrum is subjected to a magnetic field, spectral lines split.

Third Quantum Number (Magnetic Quantum Number): Determines the orientation of the orbit in space. Its values depend on l.

m = -l ... l

Fourth Quantum Number (Spin Quantum Number): Indicates the electron's intrinsic angular momentum (spin).

s = +1/2, -1/2

Quantum Mechanics

De Broglie's Hypothesis

Every moving particle has an associated wave with wavelength λ = h / (m · v).

Heisenberg Uncertainty Principle

It is impossible to simultaneously know both the momentum and position of a moving particle with perfect accuracy.

Schrödinger Equation

Schrödinger's wave equation describes the behavior of small particles. It implies that energy and wave functions are quantized.

The square of the wave function represents the probability of finding an electron in a specific region of space.

Orbitals and Quantum Numbers

Orbital: The region of space where the probability of finding an electron is highest.

Orbitals are determined by three quantum numbers:

• Principal Quantum Number (n): Indicates orbital size and energy. Takes integer values.
• Azimuthal Quantum Number (l): Indicates orbital shape and influences energy. Its values depend on n.
• Magnetic Quantum Number (m): Indicates the spatial orientation of the orbital. Its values depend on l.

A fourth quantum number, the Spin Quantum Number (s), indicates the electron's spin.

Electronic Configuration

Electronic configuration describes the arrangement of electrons within an atom's orbitals.

It follows these principles:

Principle of Minimum Energy

Electrons occupy the available orbitals with the lowest energy first, yielding the ground state electronic configuration.