Atomic Models and Experiments

Study Notes

The atom was visualized as a sphere of positive charge with negative electrons embedded within it.

Discovered by Eugen Goldstein
Positively charged particles (ions) produced from gases within specific gas-discharge tubes
Different gases produced different (e/m) values, indicating the presence of different particles.

Determined the charge on an electron in 1906
Oil droplets were sprayed between two charged plates, acquiring an electric charge.
Gravity pulled the droplets downward, while an electric field could be applied to move the droplets upward.
By balancing the electric field and gravity, specific droplets could be suspended.
The force due to gravity (mg) was equal to the force due to the electric field (Ee), where e is the charge on the droplet, m is its mass, g is acceleration due to gravity, and E is the electric field strength.

Proposed that atoms consist of a small, dense, positively charged nucleus surrounded by negatively charged electrons.
This model was unstable, as the electron should have lost energy and spiraled into the nucleus.
This model could not explain the discrete spectral lines observed in atomic emissions.

Built upon Planck's quantum theory of radiation to propose a more stable atomic model
Electrons orbit the nucleus stably without radiating energy at specific distances from the nucleus (fixed energy levels).
These energy levels are associated with definite energies, labeled with integers (1, 2, 3, etc.) or symbols (K, L, M, N, etc.).
Electrons gain or lose energy by jumping between allowed orbits, absorbing or emitting electromagnetic radiation.
The energy change during the jump is determined by Planck's equation: ΔE = E2-E1 = hν, where ν is frequency and h is Planck's constant.
Also known as the "quantum model," it explains the spectral lines in atomic emissions.

Starting from the angular momentum quantum rule (mvr = nh/2π), Bohr calculated energies of orbits in the hydrogen atom.
The attraction force between the nucleus and electron (Ze^2/r^2) equals the centripetal force (mv^2/r), where Ze is the nuclear charge, m is the electron mass, v is the electron velocity, and r is the orbital radius.
Bohr postulated that the angular momentum (mvr) is an integer multiple of ħ (nħ), where n is the principal quantum number and ħ = h/2π.
Combining these equations allows one to calculate the radius (r) and velocity (v) of the electron in a specific energy level.
The calculated energy of the electron is quantized, depending on the principal quantum number (n).

Interpreted Bohr's angular momentum quantum rule as a standing wave condition, where a whole number of wavelengths fit along the circumference of the electron's orbit (nλ=2πr).
Combining this with De Broglie's wavelength (λ = h/p) reproduces Bohr's rule (mvr= nħ).

Failed to explain spectra of larger atoms.
Violates the uncertainty principle of Heisenberg (Δp×Δx ≥ h/2π), which implies that we cannot know both the position and speed of a particle (electron) with perfect certainty.

Expanded on the quantized energy levels proposed by Bohr, leading to a more accurate model of electron motion.
Uses De Broglie's matter waves and a three-dimensional wave equation to describe electron behavior around the nucleus.
The simplest form of the Schrödinger equation is Hψ= Eψ, where ψ is the wave function, H is the Hamiltonian, and E is the energy.
Solving the equation for the hydrogen atom naturally generates quantum numbers.
The Schrödinger equation gives probabilities of finding the electron around the nucleus, rather than defining a specific orbit.

Principle quantum number (n): Determines the electron shell's size and energy level, denoted by integers 1, 2, 3, ...
Angular momentum quantum number (l): Describes the shape of the subshells and orbitals.
- l = 0: s orbitals (spherical)
- l = 1: p orbitals (dumbbell-shaped)
- l = 2: d orbitals (more complex shapes)
- l = 3: f orbitals (even more complex shapes)
Magnetic quantum number (ml): Determines the orientation of the orbitals within a subshell.

Formed due to electrostatic attraction between positively charged cations and negatively charged anions.
Often involves a metal atom (low ionization energy) losing an electron to a nonmetal atom (high electron affinity) to achieve a stable electron configuration.
The electrostatic attraction between anions and cations leads to the formation of a solid crystalline lattice with an alternating arrangement of ions.
In the case of sodium chloride (NaCl), sodium loses one electron to form Na+, and chlorine gains one electron to form Cl-, resulting in a 1:1 ratio of ions in the compound.

Generally have high melting points due to the strong electrostatic attraction between the ions.
The higher the charges of the ions, the stronger the cohesive forces and the higher the melting point.