Physics Chapter: Atomic Structure and Gas Laws

Atomic Theory

• Matter is composed of individual particles called atoms.
• The weight of a gas is the sum of the weights of all its atoms or molecules.
• There are more than 100 known elements.
• Most elements are found in nature; some are artificially produced.
• Each element has a unique number in the periodic table, for example, hydrogen (H) 1, helium (He) 2, oxygen (O) 8, and uranium (U) 92.

Atomic Number

• The symbol Z is used to represent the atomic number, which is equal to the number of protons.
• The atomic number also represents the number of electrons in an atom.
• The atomic number determines the chemical properties of an element.

Atomic Weight

• The atomic weight (M) is the weight in grams of a precise number of atoms.
• This precise number is Avogadro's number, 6.022 x 10²³.
• Generally, an element further down the periodic table has heavier atoms.
• Examples include: H - 1.008, He - 4.003, O - 16.00, and U - 238.0.
• Atomic weight is also expressed in atomic mass units (u).
• If an element's isotopic abundance is non-natural (enriched or depleted), calculate the atomic weight using a weighted sum of atomic masses of its isotopes.

Atomic Mass

• Atomic mass refers to the mass of a single atom of a particular isotope.
• Atomic weight is a weighted average of the atomic masses of all the isotopes of an element.

Hydrogen Isotopes

• Hydrogen has three isotopes: protium (¹H), deuterium (²H), and tritium (³H).
• Protium has 1 proton.
• Deuterium has 1 proton and 1 neutron.
• Tritium has 1 proton and 2 neutrons.

Atomic Number Density

• The number of atoms per cubic centimeter (N) is determined by the density (p) of a material in grams per cubic centimeter and Avogadro's number.
• The equation for atomic number density is N = (pN_A)/M.
• The equation applies to compounds and molecules, in which case M is the molecular weight.

Gases

• Gases are described by the ideal gas law: PV = nRT.
• In the equation:
• P is pressure
• V is volume
• n is the number of particles
• R is the gas constant
• T is absolute temperature
• The variable k is Boltzmann's constant.

Maxwell-Boltzmann Distribution

• Gas particles have a range of speeds (v) described by Maxwell's gas theory.
• The most probable speed (v_p) is given by: v_p = √(2kT/m).
• The average speed (v) is given by: v = √(8kT/(πm)).

The Atom and Light

• The color of a heated solid or gas changes with temperature, shifting from red (long wavelength) to blue (short wavelength).
• Light is composed of photons, discrete packets of energy.
• Energy (E) of a photon is directly proportional to its frequency (v), described by Planck's equation: E = hv.

Bohr Model

• Bohr's model explains light emission and absorption in hydrogen atoms.
• The atom consists of a single electron orbiting a positively charged nucleus (proton).
• Electrons can only exist in specific orbits with defined radii.
• When electrons jump between orbits, energy is either absorbed or emitted as a photon.
• Different orbits have different energies.
• Electron orbits are described by the principal quantum numbers n (1, 2, 3, and so on).
• The radius increases as the square of the principal quantum number (n²).
• The photon's energy is the difference between the two orbits.

Quantum Mechanics

• Quantum mechanics extends our knowledge of the atom.
• The location of an electron in an atom is described by a probability expression, not a precise trajectory.
• Heisenberg's uncertainty principle states the precise measurement of position and momentum of a particle is impossible simultaneously.

Laser Beams

• Ordinary light is a mixture of many frequencies, directions, and phases.
• Lasers emit a coherent beam of a single color.
• Lasers achieve this by stimulating emission of radiation from atoms in a controlled manner.
• Lasers emit light through a combination of reflection and stimulation within a tube.
• The reflections between mirrors in the laser enhance the light beam.

Nuclear Structure

• Most elements are composed of atoms with differing masses (called isotopes).
• Isotopes have the same atomic number (number of protons = number of electrons) but differing neutron numbers.
• Examples include the isotopes of hydrogen: ordinary hydrogen, heavy hydrogen (deuterium), and tritium.
• In isotopes, the mass number (A) signifies the total number of nucleons (protons and neutrons).
• Atomic weight is approximately equal to the mass number.
• Isotopes are denoted with a chemical symbol X with a superscripted mass number (A) and a subscripted atomic number (Z).

Nuclear Notation

• A concise form for denoting isotopes using chemical symbols with superscripted mass numbers and subscripted atomic numbers.

Sizes and Masses of Nuclei

• Nuclei have dimensions on the order of 10^-15 m (femtometers [fm]).
• Atoms have dimensions on the order of 10^-10 m (angstroms [Å]).
• The radii of nuclei are calculated by R = 1.25 x 10^-13A^1/3 cm.
• Scales used to compare atom masses measure the isotope of carbon-12 (12C) as 12 units.

Mass Defect

• Nuclei are lighter than the sum of their constituent nucleons.
• The difference in mass is the mass defect (∆m).
• The mass defect calculation uses the following formula: ∆m = (N_nm_n + Zm_H) − M.

Binding Energy

• The energy needed to separate a nucleus into its component neutrons and protons.
• The binding energy of a nucleus is given by BE = ∆mc².
• Binding energies are calculated by using empirical formulas and the Bethe-Weizsäcker formula.

Binding Energy per Nucleon

• The binding energy per nucleon provides insight into the relative stability of a nucleus.
• Nuclei with higher binding energy per nucleon are more stable.
• The graph illustrates that nuclei near iron (⁵⁶Fe) have the highest BE/A, signifying they are highly stable.

Magic Numbers

• Certain numbers of protons or neutrons in a nucleus result in a structure with complete shells, which is called the magic number.
• Magic numbers exhibit high binding energy per nucleon.
•  Some common magic numbers are 2, 8, 20, 28, 50, 82, and 126.