Chapter 1 Atoms: The Quantum World

Investigating Atoms

how were goals in this chapter is to understand theories about atoms structure and understand our stuff to explore this structure by watching radiation and understand the whole picture radiation and particles

The Nuclear Model of the Atom

how to Describe the experiments that led to the formulation of the
nuclear model of the atom:

Electromagnetic Radiation

electromagnetic radiation, in classical physics, the flow of energy at the universal speed of light through free space or through a material medium in the form of the electric and magnetic fields that make up electromagnetic waves

2 quation ofrelations between wavelength or frequency of light speed

we can use prank constant to calculate the energy of radiation we duplicated between the frequency and Planck constant

how to use planck constant to calculate the energy of photons wave

Wien’s Displacement Law

3 Use Wien’s law to estimate a temperature

Wien’s displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.

Photon Model of Light

Atomic Spectra

until now we deal on the photons now we mix between the characters of particles and radiation and we deal about the atoms

Atomic spectra are defined as. The spectrum of the electromagnetic radiation emitted or absorbed by an electron during transitions between different energy levels within an atom. When an electron gets excited from one energy level to another.

Atomic spectra refer to the characteristic patterns of electromagnetic radiation emitted or absorbed by atoms or molecules. These spectra are essential in studying the energy levels and electronic structure of atoms and molecules. There are two main types of atomic spectra: emission spectra and absorption spectra.

1. Emission Spectra:
   • Emission spectra are produced when atoms or molecules emit electromagnetic radiation as they transition from higher energy levels to lower energy levels.
   • The emitted radiation corresponds to the energy difference between the initial and final energy levels of the electron within the atom or molecule.
   • Emission spectra are often observed as discrete lines or bands of light at specific wavelengths, representing the energy levels of the emitting species.
   • Examples of emission spectra include the line spectra of hydrogen atoms (Balmer series, Lyman series, etc.) and the atomic emission spectra of elements in flames or gas discharge tubes.
2. Absorption Spectra:
   • Absorption spectra are produced when atoms or molecules absorb specific wavelengths of electromagnetic radiation as they transition from lower energy levels to higher energy levels.
   • The absorbed wavelengths correspond to the energy required to promote electrons from lower energy levels to higher energy levels within the atom or molecule.
   • Absorption spectra are observed as dark lines or bands in a continuous spectrum, indicating the wavelengths that have been absorbed by the sample.
   • Examples of absorption spectra include the absorption lines seen in the solar spectrum due to absorption by elements in the Sun’s atmosphere and the absorption spectra of gases in laboratory experiments.

The material features of a substance can significantly influence its atomic spectra. Here’s how:

1. Chemical Composition:
   • The atomic spectra of a material depend on the types of atoms or molecules present and their electronic structure.
   • Different elements or compounds will have distinct emission and absorption spectra based on their unique energy levels and transitions.
2. Temperature and Pressure:
   • The temperature and pressure of a material can affect its atomic spectra. For example, at higher temperatures, atoms may be excited to higher energy levels, leading to changes in the observed emission or absorption lines.
   • Pressure can also influence spectral lines, especially in gases, due to collisional broadening or narrowing of the lines.
3. External Fields:
   • External electric or magnetic fields can modify atomic spectra through Stark effect (electric field) or Zeeman effect (magnetic field), causing shifts or splitting of spectral lines.
   • These effects are important in spectroscopic techniques such as Stark spectroscopy and Zeeman spectroscopy.
4. Physical State:
   • The physical state of a material (solid, liquid, gas) can affect its atomic spectra due to differences in molecular interactions, crystal structure, and environment.
   • For example, gas-phase atoms may exhibit narrower spectral lines compared to atoms in a condensed phase due to reduced collisional broadening.

In summary, the atomic spectra of a material are influenced by its chemical composition, temperature, pressure, external fields, and physical state. These spectra provide valuable information about the energy levels, electronic transitions, and properties of atoms and molecules, making them essential in fields such as chemistry, physics, astronomy, and materials science.

The Bohr model of the hydrogen atom,

The Bohr model of the hydrogen atom, proposed by Niels Bohr in 1913, was a significant advancement in understanding atomic structure and the behavior of electrons within atoms. It was a crucial step towards the development of modern quantum mechanics.

Key features of the Bohr model of the hydrogen atom:

1. Quantized Electron Orbits: Bohr proposed that electrons orbit the nucleus of a hydrogen atom in quantized orbits, meaning that only certain specific orbits are allowed. Each orbit corresponds to a specific energy level. The orbits are labeled by an integer n, known as the principal quantum number, where n=1,2,3,….
2. Energy Levels: The energy of an electron in a particular orbit is quantized and is given by the formula:

5. Stability of Orbits: According to the Bohr model, electrons in stable orbits do not emit radiation and are thus stable. Radiation is emitted or absorbed only during transitions between orbits.

6. Limitations and Extensions: While the Bohr model successfully explained many features of the hydrogen atom’s spectrum (such as the Balmer series), it had limitations, such as its inability to fully explain the fine structure of spectral lines and the behavior of multi-electron atoms. These limitations were addressed and resolved with the development of quantum mechanics.

The Bohr model laid the foundation for the later development of quantum mechanics, which provided a more comprehensive and accurate description of atomic structure and behavior. Despite its limitations, the Bohr model remains an important historical milestone in the understanding of atomic physics and continues to be taught as a foundational concept in introductory chemistry and physics courses.

Quantum Theory

The Stefan Boltzmann Law

The Stefan-Boltzmann law is a physical law that states that the radiation flux emitted by a black body is proportional to the fourth power of its temperature.

Radiation, Quanta, and Photons- The Wave-Particle Duality of Matter

The Uncertainty Principle

Heisenberg’s uncertainty principle is a fundamental principle in quantum mechanics, according to which it is not possible to simultaneously determine exact values for pairs of measurable variables of a single elementary particle, even if the measuring instruments have infinite precision. This principle was published in 1927 by Nobel Prize winning physicist Werner Heisenberg and has been named after him ever since.

Wavefunctions and Energy

Levels

Electron Configuration

what is the method to write Electron Configuration to element in the periodic table?

To write the electron configuration of an element in the periodic table, you follow a set of rules based on the Aufbau principle, Pauli exclusion principle, and Hund’s rule. These rules help you determine the distribution of electrons in the various energy levels (shells) and orbitals of an atom. Here is a step-by-step method to write the electron configuration of an element:

1. Determine the Atomic Number: The atomic number of an element tells you the number of protons in its nucleus and is also equal to the number of electrons in a neutral atom of that element. You can find the atomic number of an element on the periodic table.
2. Fill Electrons in Energy Levels (Shells): Start by filling electrons into the energy levels (shells) around the nucleus. The energy levels are designated by the principal quantum number, n, where n=1,2,3,…. The first energy level (n=1) is closest to the nucleus and can hold a maximum of 2 electrons, the second energy level (n=2) can hold up to 8 electrons, and so on.
3. Use the Aufbau Principle: The Aufbau principle states that electrons fill the lowest energy levels and orbitals first before moving to higher energy levels. Within an energy level, electrons fill orbitals based on increasing energy.
4. Fill Electrons in Sublevels (Orbitals): Each energy level is divided into sublevels or orbitals based on the azimuthal quantum number, l, which determines the shape of the orbital. The possible sublevels are designated as s, p, d, and f.
   • The s sublevel has one orbital and can hold a maximum of 2 electrons.
   • The p sublevel has three orbitals and can hold a maximum of 6 electrons.
   • The d sublevel has five orbitals and can hold a maximum of 10 electrons.
   • The f sublevel has seven orbitals and can hold a maximum of 14 electrons.
5. Apply Pauli Exclusion Principle: The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. Therefore, each orbital can hold a maximum of 2 electrons with opposite spins (up and down).
6. Use Hund’s Rule: Hund’s rule states that electrons occupy orbitals singly (with the same spin) before pairing up. This means that electrons will fill empty orbitals in the same sublevel before pairing up in the same orbital.

The Wavefunction and Its Interpretation The Quantization of Energy

The Hydrogen Atom

Energy Levels

Atomic Orbitals

Quantum Numbers, Shells, and Subshells

The wave function quantum numbers.

1. N- how many energy levels must have integer values
   orbitals
   S- count
   F- An endless sign
   D- Flower
   F- Nonsense
   H.G
2. L – quantum number of angular tena
   Angular momentum of n
   Dependent N can have values of N minus 1 including 0
3. M magnetic quantum number =
   L 1 includes 0 but also less positive and negative and 0
4. Spin number = flat half or minus half
   2 electrons can be found in each of the orbitals
   Number of electrons that will occupy an orbital = 2N^2

The Shapes of Orbitals

Electron Spin

The Electronic Structure of Hydrogen

Many-Electron Atoms

Orbital Energies

The Building-Up Principle

Topic IF Periodicity IM The General Structure of the

Periodic Table

• Atomic Radius
• Ionic Radius
• Ionization Energy
• Electron Affinity

The Inert-Pair Effect

Diagonal Relationships

F.B The General Properties of the

Resonance Structures

Quantum Numbers