Atomic Structures

INTRODUCTION TO MODERN PHYSICS

ATOMIC MODELS

In the 18th and 19th centuries, scientists developed various atomic models to explain atomic structure. Each model contributed to the modern understanding of the atom.

John Dalton's Model (Early 1800s)

Key Postulates:

• All matter is composed of atoms.
• Atoms are indivisible.
• Atoms of the same element are identical and have a constant mass unique to that element.
• Atoms rearrange during chemical reactions.
• Atoms cannot be created or destroyed, but can be transformed from one form to another.

Thomson Atomic Model (Early 1900s)

Postulated by Sir Joseph John Thomson after the discovery of electrons.

• Described the atom as a positively charged sphere with negatively charged electrons embedded within it.
• Commonly known as the "plum pudding model", where the pudding is the positive charge and the plums are the electrons.

Rutherford Atomic Model (Early 1900s)

Modified by Rutherford after discovering the nucleus, based on the alpha ray scattering experiment.

Deductions:

• Most of the atom is empty space.
• The nucleus is at the center, concentrating most of the charge and mass.
• The atom is spherical.
• Electrons surround the nucleus and revolve in circular orbits, similar to planets orbiting the sun (Planetary model).

Limitation: According to classical physics, electrons revolving in circular orbits would accelerate, expend energy, and eventually collapse into the nucleus.

Bohr's Atomic Model (1915)

Proposed by Niels Bohr, this is one of the most widely used atomic models.

Summary of Bohr's Theory:

• Electrons are placed in discrete orbits called “stationary orbits” or shells.
• Each orbit (shell) has a fixed energy.
• Energy levels of these shells are represented by quantum numbers (n: 1, 2, 3, 4... or K, L, M, N...).
• Electrons can jump to higher energy levels by absorbing energy and move to lower levels by losing or emitting energy.
• If an electron remains in its stationary orbit, there is no absorption or emission of energy.
• Electrons revolve around the nucleus only in these stationary orbits.
• The energy of the stationary orbits is quantized.

ATOMIC STRUCTURE

Atoms are the ultimate building blocks of all matter, composed of three main subatomic particles:

• Protons: Positively charged (1.673 × 10-27 kg mass).
• Neutrons: Electrically neutral (1.675 × 10-27 kg mass).
• Electrons: Negatively charged (9.109 × 10-31 kg mass, almost 2000 times lighter than proton/neutron).

The nucleus of an atom is made up of protons and neutrons, while electrons surround it.

• Atomic Number (Z): The number of protons in the nucleus. It uniquely characterizes an element (e.g., Hydrogen Z=1, Helium Z=2). In a neutral atom, Z also equals the number of electrons.
• Ions: Formed when atoms gain or lose electrons to increase stability, resulting in a net electrical charge.

Different elements have unique atomic structures due to varying numbers of protons, electrons, and neutrons, which leads to their distinct characteristics.

ATOMIC ISOTOPES

While each element has a unique atomic number (number of protons), an element can have different atomic structures based on the total number of nucleons (protons + neutrons).

• Isotopes: Variants of an element that have the same number of protons (same atomic number Z) but different numbers of neutrons (and thus different mass numbers A).
• Notation: Represented as AZX, where A is the mass number and Z is the atomic number.
• Example: Hydrogen has three naturally occurring isotopes:
  • Protium (11H): 1 proton, 0 neutrons (Mass number: 1)
  • Deuterium (21H): 1 proton, 1 neutron (Mass number: 2)
  • Tritium (31H): 1 proton, 2 neutrons (Mass number: 3)
• Isotopes generally exhibit similar chemical behavior due to the same electronic structure but can vary in stability.

ARRANGEMENT OF ELECTRONS (SHELL MODEL)

Electrons orbit the nucleus at specific distances, forming electron shells.

• Electron Shell: A group of atomic orbitals with the same principal quantum number (n).
• Each shell contains a fixed number of electrons and is associated with a particular range of electron energy.
• Inner shells must be completely filled before electrons occupy outer shells.
• Valence Electrons: Electrons in the outermost shell. They have higher energy and primarily determine an atom's chemical properties and its behavior as a conductor.
• Energy Transitions:
  • Electrons can absorb energy (in the form of a photon) to jump to an outer shell (atomic excitation) or break free (ionization).
  • If an electron loses energy, it moves to an inner shell, causing a photon to be emitted.
• The number of valence electrons corresponds to the element's group in the periodic table.

ATOMIC ABSORPTION AND EMISSION

• Ground State: The lowest energy state of an atom, where electrons are arranged to minimize total energy.
• Absorption: When atoms gain energy (e.g., from light), electrons absorb this energy and move to discrete, higher energy levels.
• Excited State: A state where an atom's potential energy is higher than its ground state. Excited atoms are unstable.
• Emission: When an atom in an excited state returns to a lower energy level (or ground state), it releases the excess energy, often as electromagnetic radiation (photons) or heat.

ATOMIC SPECTRA

Atomic spectra are defined as the spectrum of electromagnetic radiation emitted or absorbed by electrons during transitions between different energy levels within an atom.

There are three types of atomic spectra:

• Continuous Spectrum: Contains all wavelengths of light within a given range (e.g., stars emit continuous spectra based on their temperature).
• Emission Spectrum: Produced when an excited cloud of gas emits light. It consists of a series of colored lines at specific wavelengths, dependent on the gas's temperature, density, and composition.
• Absorption Spectrum: Produced when light passes through a gas, and certain wavelengths are absorbed. It appears as dark lines or gaps in a continuous spectrum, corresponding to the wavelengths absorbed by the gas.

Atoms can be excited by various sources, such as electrical currents (e.g., noble gases producing distinctive colors) or heat (e.g., metal chlorides in flames). Each element produces a unique "signature" color or spectral pattern due to its specific electron configurations and excitation possibilities.

ATOMIC SPECTROSCOPY

Atomic spectroscopy is the study of electromagnetic radiation absorbed or emitted by atoms. It has three main types:

• Atomic Emission Spectroscopy (AES):
  • Principle: Excited atoms emit light at characteristic wavelengths as they return to a lower energy state.
  • Applications: Environmental samples, metallurgical analysis, biological tissues.
• Atomic Absorption Spectroscopy (AAS):
  • Principle: Ground-state atoms in a gaseous state absorb radiation at specific frequencies corresponding to electronic transitions. Requires identical energy differences between levels for absorption.
  • Applications: Heavy metal analysis in water, blood, food.
• Atomic Fluorescence Spectroscopy (AFS):
  • Principle: Atoms absorb radiation and then re-emit it as fluorescence. It combines aspects of both atomic emission and absorption, involving both excitation and de-excitation.
  • Applications: Trace analysis of elements like mercury, arsenic, selenium.

CATHODE RAY

A cathode ray is a stream of electrons emitted from the negative electrode (cathode) in a discharge tube containing a gas at low pressure.

Production:

• Electrons orbit every atom's nucleus and can move as electric current.
• In a discharge tube, a potential difference (voltage) applied across electrodes causes electrons from the cathode to accelerate.
• When these electrons strike certain molecules (e.g., a coating on a screen), they cause the molecules to emit light, creating a glow.

Properties of Cathode Rays:

• They are negatively charged.
• They travel in a straight line.
• They ionize the gas inside the tube.

Cathode Ray Tube (CRT)

• Inventor: Karl Ferdinand Braun (1897); earlier versions were called gas discharge tubes or Crookes tubes.
• Structure: An evacuated glass envelope containing an electron gun (source of electrons) and a fluorescent screen. Internal or external means accelerate and redirect electrons.
• Operation: A potential difference accelerates electrons from the cathode towards an anode. These electrons excite gas atoms (in older tubes) or directly strike a fluorescent screen (in modern CRTs).
• Function: In modern CRTs (e.g., Coolidge tube), an electron beam is focused by focusing coils and deflected by electric or magnetic fields to create a visual trace or image on a phosphor-coated screen. When accelerated electrons hit the screen, their kinetic energy is converted into light and heat.
• Applications: Cathode-ray oscilloscopes (monitoring voltages/currents), picture tubes for televisions and computer monitors, radar displays, X-ray production (when focused on a hard target), and even cathode-ray furnaces for high temperatures.

X-rays

X-rays were discovered by Wilhelm Conrad Röntgen in 1895, named "X-radiation" for their unknown nature. They are a form of electromagnetic radiation with short wavelength.

Production and Properties of X-ray:

There are three common mechanisms to produce X-rays:

1. Acceleration of a charged particle: As in a Coolidge tube.
2. Atomic transitions: Electrons moving between discrete energy levels within an atom.
3. Radioactive decay: Of some atomic nuclei.

Coolidge Tube for X-ray production:

• Mechanism: Fast-moving electrons are suddenly stopped by a solid target.
• Components:
  • Cathode: A heated tungsten filament (by a low-tension battery) emits thermionic electrons.
  • Anode/Target: Electrons are accelerated towards a target (often tungsten) by a high potential difference. The target material has a high melting point and a high atomic number to produce more energetic and intense X-rays.
• Intensity: Controlled by the number of electrons striking the target per second (proportional to filament temperature/current).
• Frequency: Depends on the voltage between the cathode and anode.

Types of X-rays:

• Bremsstrahlung (Braking radiation): Produced when electrons decelerate or "brake" upon hitting the anode. Most effective when small, charged particles interact with large atoms (e.g., in a Coolidge tube).
• Characteristic X-rays: Emitted as photons when electrons change from one atomic orbit to another. These photon energies are characteristic of the specific atom and can be used to identify small quantities of elements.

Radioactive disintegration of radionuclides is also a source of X-rays.

RADIOACTIVITY

Radioactivity was discovered by Henri Becquerel in 1896 when he observed that Uranium salt crystals emitted invisible radiation that could darken photographic plates.

• Definition: The spontaneous disintegration of unstable atomic nuclei to form more energetically stable atomic nuclei. This process involves the unstable nucleus losing particles or releasing energy.

Properties of Radioactivity:

• Spontaneous: Occurs naturally without external stimulation.
• Unaffected by external agents: Not influenced by temperature, pressure, electric fields, or magnetic fields.
• Accompanied by emission: Involves the emission of electrons (e-), positrons (e+), alpha particles (4He2), photons (gamma rays), and other particles.

Sources of Nuclear Instability:

• Atoms with a large atomic number (Z) often need more neutrons than protons to overcome the electrostatic repulsion between protons and maintain nuclear stability.
• Beyond a certain point, increasing neutrons is insufficient to counteract proton repulsion, leading to nuclear instability.
• Unstable nuclei undergo decay by ejecting excess nucleons or other particles, or by releasing energy, to transform into more stable nuclei. This may involve a series of decays.
• During radioactive decay, the principles of conservation of energy, momentum, charge, and nucleon number apply.

Different Channels of Radioactive Decay:

1. Alpha Decay (α-decay):
   • Emission: An alpha particle (4He2), consisting of 2 protons and 2 neutrons.
   • Effect: The parent nucleus (AZX) disintegrates into a lighter daughter nucleus (A-4Z-2Y). The atomic number (Z) decreases by 2, and the mass number (A) decreases by 4. The daughter element (Y) is different from the parent (X).
   • Equation: AZX → A-4Z-2Y + 42He
2. Beta Decay (β-decay):
   • Beta minus Decay (β-):
     • Emission: A beta minus particle (0-1e), which is an electron, along with an antineutrino.
     • Mechanism: A neutron in the nucleus converts into a proton and an electron (n → p + e- + ν̅e).
     • Effect: The mass number (A) remains the same, but the atomic number (Z) increases by 1 (AZX → AZ+1Y + 0-1e + ν̅e).
     • Example: 125B → 126C + β- + ν̅e
   • Beta plus Decay (β+):
     • Emission: A beta plus particle (0+1e), which is a positron, along with a neutrino.
     • Mechanism: A proton in the nucleus converts into a neutron and a positron (p → n + e+ + νe).
     • Effect: The mass number (A) remains the same, but the atomic number (Z) decreases by 1 (AZX → AZ-1Y + 0+1e + νe).
     • Condition: Only possible if the atomic mass of the parent nucleus is greater than that of the daughter nucleus by at least two electron masses (equivalent to 1.02 MeV of energy).
     • Example: 127N → 126C + β+ + νe
   • Electron Capture (EC):
     • Mechanism: An inner-shell atomic electron is captured by the nucleus, converting a proton into a neutron (p + e- → n + νe). This occurs when there's an excess of protons but insufficient energy for β+ decay.
     • Effect: The mass number (A) remains the same, but the atomic number (Z) decreases by 1 (AZX + 0-1e → AZ-1Y + νe).
     • Consequence: When an outer-shell electron fills the vacancy left by the captured electron, characteristic X-rays of the daughter element are emitted.
     • Example: 74Be + 0-1e → 73Li
3. Gamma Decay (γ-decay):
   • Emission: A gamma (γ) photon, which is high-energy electromagnetic radiation.
   • Mechanism: An excited nucleus transitions from a higher energy state (denoted with an asterisk, e.g., AZX*) to a lower energy state.
   • Effect: Gamma rays carry no charge or mass. Thus, neither the atomic number (Z) nor the mass number (A) of the nucleus changes. The nuclide remains the same; only its energy state changes.
   • Energy: The energy of the γ photon is given by hf = Ei - Ef (initial minus final energy of the nucleus).
   • Equation: AZX* → AZX + γ

BINDING ENERGY AND MASS DEFECT

When subatomic particles combine to form an atom or nucleus, there's a difference between the sum of their individual masses and the mass of the resulting composite particle.

Binding Energy:

• The extra energy obtained when an atom is assembled from its components.
• Alternatively, the energy that must be supplied to disassemble an atom into its components.
• Example (Hydrogen atom): The rest energy of a combined hydrogen atom (mHc2) is less than the sum of the rest energies of a separated proton and electron (mpc2 + mec2) by 13.6 eV. This 13.6 eV is the binding energy of the hydrogen atom.
  • mpc2 + mec2 = mHc2 + 13.6 eV
  • mpc2 + mec2 - mHc2 = 13.6 eV (Binding Energy)

Mass Defect (Δm):

• Nuclear experiments show that the total mass of a nucleus (Mnucl) is less than the sum of the masses of its constituent nucleons (protons and neutrons).
• Mnucl < Zmp + Nmn, where Zmp is the total mass of protons and Nmn is the total mass of neutrons.
• The mass difference (Δm) is called the mass defect, and is given by:
  • Δm = (Zmp + Nmn) - Mnucl
• This "missing mass" is converted into the nuclear binding energy that holds the nucleus together, as described by Einstein's mass-energy equivalence principle.
• Einstein's relation: E = mc2, so Binding Energy = Δmc2.

Nuclear binding energy is crucial because it represents the energy required to keep the protons and neutrons within a nucleus intact, and also the immense energy released during nuclear fission or fusion reactions.

NUCLEAR FISSION AND FUSION

Nuclear Fission:

• Definition: The splitting of a heavy nucleus into two or more lighter nuclei.
• Discovery: In 1938, Otto Hahn, Lise Meitner, and Fritz Strassmann bombarded uranium with neutrons, observing lighter elements like barium formed.
• Example: Neutron-induced fission of Uranium-235:
  • 23592U + 10n → 14156Ba + 9236Kr + 3 10n
• Characteristics:
  • Usually divides asymmetrically, producing different sets of products each time.
  • Releases more than one neutron per fission event.
  • Nuclear Chain Reaction: If released neutrons induce fission in other neighboring nuclei, a self-sustaining series of fission reactions occurs.
  • A minimum mass (critical mass) of fissile isotope is required to sustain a chain reaction; otherwise, too many neutrons escape.

Nuclear Fusion:

• Definition: A process in which two light nuclei combine to produce a heavier, more stable nucleus.
• Energy Barrier: The positive charges of the nuclei create a large electrostatic energy barrier (Coulomb barrier) that must be overcome.
• Condition: Nuclei need sufficient kinetic energy (extremely high temperatures) to approach close enough for the strong nuclear force to initiate fusion.
• Energy Release: Fusion reactions are highly exothermic for the lightest elements (e.g., the energy source in the sun and stars).
• Examples:
  • Deuterium-Deuterium (D-D) fusion: Two deuterium atoms combine to produce helium-3 and a neutron.
    • 21H + 21H → 32He + 10n
  • Deuterium-Tritium (D-T) fusion: A deuterium atom and a tritium atom fuse to produce helium-4 and a neutron.
    • 21H + 31H → 42He + 10n

Both fission and fusion involve nuclear reactions where the total mass of the products is different from the total mass of the reactants. This mass difference is converted into an enormous amount of energy, as dictated by E=mc2. Fusion generally releases significantly more energy per unit mass than fission.