Atoms and Atomic Theory

The Law of Multiple Proportions

The law of multiple proportions was formulated by John Dalton in 1804. It states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.

• Example: Carbon monoxide (CO) and carbon dioxide (CO2) both contain carbon and oxygen.

• In CO, the mass ratio of oxygen to carbon is 1.33:1 (1.33 g O per 1 g C).

• In CO2, the mass ratio is 2.67:1 (2.67 g O per 1 g C).

• The ratio of oxygen masses that combine with 1 g of carbon in the two compounds is 2.67/1.33 = 2:1, a simple whole number ratio.

Problem Example: For NO2 and N2O, the mass of O to 1 g N in NO2 is 2.28 g, and in N2O is 0.570 g. The ratio is 2.28/0.570 = 4:1.

Dalton's Atomic Theory

John Dalton's atomic theory provided a framework for understanding chemical laws:

• 1. Each element is composed of tiny, indestructible particles called atoms.

• 2. All atoms of a given element have the same mass and properties.

• 3. Atoms combine in simple, whole-number ratios to form compounds.

• 4. Atoms of one element cannot change into atoms of another element in a chemical reaction.

Discovery of Subatomic Particles

The Electron

J.J. Thomson discovered the electron through cathode ray experiments:

• Cathode rays are streams of negatively charged particles (electrons) traveling from the negative electrode (cathode) to the positive electrode (anode).

• Properties of cathode rays:

  • Travel in straight lines

  • Independent of the material of the cathode

  • Carry a negative charge

• Charge-to-mass ratio measured as C/g.

The Proton and Neutron

• Protons are positively charged particles found in the nucleus.

• Neutrons are uncharged particles in the nucleus with a mass nearly equal to that of protons.

• Protons and neutrons each have a mass of approximately 1 atomic mass unit (amu).

The Nuclear Model of the Atom

Ernest Rutherford's gold foil experiment led to the nuclear model:

• Most of the atom's mass and all its positive charge are concentrated in a small nucleus.

• Most of the atom's volume is empty space, with electrons moving around the nucleus.

• In a neutral atom, the number of protons equals the number of electrons.

Atomic Number, Mass Number, and Isotopes

• Atomic number (Z): Number of protons in the nucleus; defines the element.

• Mass number (A): Total number of protons and neutrons in the nucleus.

• Isotopes: Atoms of the same element with different numbers of neutrons.

• Symbolic notation: , where X is the chemical symbol.

Example: Chlorine-35:

Ions

• Cations: Positively charged ions formed by losing electrons (e.g., Li+ has 3 protons, 2 electrons).

• Anions: Negatively charged ions formed by gaining electrons (e.g., Cl- has 17 protons, 18 electrons).

• In a neutral atom: number of electrons = number of protons.

Atomic Mass and Molar Mass

• Atomic mass (atomic weight): Weighted average of the masses of all isotopes of an element, as found on the periodic table.

• Molar mass: Mass of one mole of a substance (in grams per mole), numerically equal to the atomic or molecular mass in amu.

• Avogadro's number: particles per mole.

Example: 12.01 g of carbon = 1 mole of carbon = atoms.

The Quantum-Mechanical Model of the Atom

Wave-Particle Duality of Electrons and Light

Electrons and light exhibit both wave-like and particle-like properties, a concept known as wave-particle duality.

• Electrons are extremely small and behave similarly to light.

• Much of atomic behavior is determined by the properties of electrons.

The Nature of Light

• Electromagnetic radiation: Light is a form of energy that travels through space at a constant speed.

• Speed of light in vacuum: m/s.

• Amplitude: Height of the wave (node to crest or trough).

• Wavelength (\lambda): Distance between successive crests or troughs; determines color.

• Frequency (\nu): Number of waves passing a point per second (Hz or s-1).

• Relationship:

Color and Energy

• Color of light is determined by its wavelength or frequency.

• White light contains all visible wavelengths; objects appear colored based on which wavelengths they reflect.

• Total energy of a wave depends on amplitude and frequency.

• Wavelength and frequency are inversely proportional: as one increases, the other decreases.

Wave Interference

• Constructive interference: Waves in phase combine to make a larger wave.

• Destructive interference: Waves out of phase cancel each other out.

• Two-slit interference: Light passing through two slits creates an interference pattern of bright and dark bands.

The Photoelectric Effect

Einstein explained the photoelectric effect as the emission of electrons from a metal surface when light shines on it.

• Electrons emitted are called photoelectrons.

• Light energy is quantized in packets called photons.

• Threshold frequency: minimum frequency needed to eject electrons.

• Energy of a photon: or , where J·s (Planck's constant).

• Kinetic energy of ejected electron:

Atomic Spectra

• Atoms absorb energy and release it as light of specific wavelengths, producing a line spectrum unique to each element.

• Line spectra are used to identify elements.

The Bohr Model of the Atom

• Electrons travel in fixed orbits at set distances from the nucleus.

• Electrons emit or absorb energy when they move between orbits.

• Energy transitions correspond to the emission or absorption of photons.

Wave Behavior of Electrons

• De Broglie proposed that particles, such as electrons, have wave-like properties.

• Only very small particles exhibit significant wave character.

Heisenberg Uncertainty Principle

• It is impossible to know both the exact position and momentum (speed) of an electron simultaneously.

• The more precisely one property is known, the less precisely the other can be known.

• This leads to indeterminacy: only the probability of finding an electron in a region can be predicted.

Schrödinger's Equation and Quantum Numbers

• Schrödinger's equation calculates the probability of finding an electron with a certain energy at a certain location.

• Solutions to the equation yield quantum numbers that describe electron properties:

  • n: Principal quantum number (energy level)

  • l: Angular momentum quantum number (orbital shape)

  • ml: Magnetic quantum number (orbital orientation)

  • ms: Spin quantum number (electron spin direction)

Summary Table: Subatomic Particles

Key Equations

• Speed of light:

• Photon energy:

• Photon energy (wavelength):

• Kinetic energy (photoelectric effect):

• Mass number: (where Z = protons, N = neutrons)

• Number of particles in a mole: (where )