Unit 1: Development of the Atomic Model

The concept of the atom dates back to ancient Greece. Around the 5th century BC, the Greek philosophers Democritus and his mentor Leucippus proposed that all matter is composed of tiny, indivisible particles. Democritus called these fundamental particles "atomos," meaning "uncuttable" or "indivisible."

Their theory, while philosophical and not based on experimental evidence, laid the groundwork for later scientific thought. Key ideas from Democritus included:

• All matter consists of atoms, which are solid, homogeneous, indivisible, and eternal.
• Atoms are constantly in motion.
• Different types of atoms have different shapes and sizes, which account for the different properties of substances. For example, sweet substances might have smooth atoms, while bitter substances might have sharp, jagged atoms.
• Between atoms lies empty space (the void).

In the early 19th century, John Dalton, an English chemist, revived and refined the atomic concept, transforming it from a philosophical idea into a scientific theory supported by experimental observations, particularly the Law of Multiple Proportions. His atomic theory, proposed in 1803, laid the foundation for modern chemistry.

Dalton's Atomic Theory consisted of several postulates:

1. All matter is composed of extremely small, indivisible particles called atoms.
2. Atoms of a given element are identical in mass, size, and other properties; atoms of different elements differ in mass, size, and other properties.
3. Atoms cannot be subdivided, created, or destroyed.
4. Atoms of different elements combine in simple whole-number ratios to form chemical compounds.
5. In chemical reactions, atoms are combined, separated, or rearranged.

While revolutionary, later discoveries led to modifications of Dalton's theory:

• Atoms are divisible: The discovery of subatomic particles (electrons, protons, neutrons) by Thomson, Rutherford, and Chadwick proved that atoms are indeed divisible.
• Atoms of the same element are not always identical: The discovery of isotopes (atoms of the same element with different numbers of neutrons, hence different masses) by Soddy showed that atoms of the same element can have different masses.
• Atoms can be transformed: Nuclear reactions (like radioactive decay and nuclear fusion/fission) demonstrate that atoms can be converted into other types of atoms, contradicting the idea that atoms cannot be created or destroyed.

In 1897, J.J. Thomson conducted experiments using cathode ray tubes, which led to the discovery of the electron. He observed that when metals were heated in sealed tubes, they emitted negatively charged particles that were much smaller than the smallest known atom. This groundbreaking discovery proved that atoms were not indivisible, as Dalton had proposed, but contained even smaller, negatively charged subatomic particles.

Based on his findings, Thomson proposed the "plum pudding" model of the atom:

• The atom is a sphere of uniformly distributed positive charge.
• Negatively charged electrons are embedded within this positive sphere, much like plums (or raisins) in a pudding.
• The total positive charge is equal to the total negative charge, making the atom electrically neutral overall.

In 1909, Ernest Rutherford and his students, Hans Geiger and Ernest Marsden, conducted the famous gold foil experiment (also known as the Geiger-Marsden experiment). They bombarded a thin sheet of gold foil with positively charged alpha particles. Their observations dramatically contradicted Thomson's plum pudding model.

Observations of the Gold Foil Experiment:

• Most alpha particles passed straight through the gold foil with little or no deflection.
• A small percentage of alpha particles were deflected at very large angles.
• A very tiny fraction (about 1 in 8000) of alpha particles were deflected back towards the source.

Rutherford's Conclusions and Nuclear Model: Rutherford famously remarked that this was "quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you." Based on these observations, Rutherford proposed the nuclear model of the atom:

• The atom consists mostly of empty space. This explains why most alpha particles passed straight through.
• The atom's positive charge and nearly all of its mass are concentrated in a very small, dense central region called the nucleus. This explains the large-angle deflections and backscattering of the positively charged alpha particles (repulsion from the positive nucleus).
• Negatively charged electrons orbit the nucleus in a large volume of space, much like planets orbiting the sun. Their small mass meant they would not significantly deflect the alpha particles.

In 1913, Niels Bohr, a Danish physicist, proposed a new model for the hydrogen atom that addressed the stability problem of Rutherford's model and explained the observed line spectra of elements. Bohr incorporated ideas from quantum theory (specifically, Planck's quantization of energy) into Rutherford's nuclear model.

Key Postulates of Bohr's Model:

1. Electrons orbit the nucleus in specific, fixed circular paths called stationary states or energy levels (also known as shells). Each energy level has a distinct, quantized energy.
2. Electrons do not radiate energy when they are in these stationary states.
3. Electrons can only move between these allowed energy levels by absorbing or emitting a specific amount of energy (a quantum or photon). When an electron moves from a lower to a higher energy level, it absorbs energy. When it moves from a higher to a lower energy level, it emits energy, often as light.
4. The energy of the emitted or absorbed photon is equal to the difference in energy between the two energy levels involved in the transition ($E_{photon} = |E_{final} - E_{initial}| = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency).

Bohr's model successfully explained the line spectrum of hydrogen and introduced the concept of quantized energy levels. It was a major step towards quantum mechanics. However, it had limitations:

• It only accurately predicted the spectra for hydrogen and other one-electron species (like He⁺, Li²⁺).
• It could not explain the spectra of multi-electron atoms.
• It did not account for the splitting of spectral lines in the presence of a magnetic field (Zeeman effect).
• It treated electrons as particles orbiting in fixed paths, which was later found to be inaccurate by the wave-particle duality of matter.

The quantum mechanical model (also known as the wave mechanical model), developed primarily by Erwin Schrödinger in 1926, along with contributions from Werner Heisenberg and others, is the most sophisticated and widely accepted model of the atom today. It builds upon the ideas of Bohr but moves beyond the concept of fixed electron orbits.

Key Features of the Quantum Mechanical Model:

• Wave-Particle Duality: It recognizes that electrons exhibit both wave-like and particle-like properties (De Broglie hypothesis).
• Heisenberg Uncertainty Principle: It states that it is impossible to know simultaneously both the exact position and the exact momentum of an electron. This means we cannot pinpoint an electron's exact path.
• Atomic Orbitals: Instead of fixed orbits, electrons exist in atomic orbitals, which are three-dimensional regions around the nucleus where there is a high probability of finding an electron. These orbitals are described by mathematical wave functions ($\psi$).
• Quantum Numbers: Each electron in an atom is described by a unique set of four quantum numbers ($n, l, m_l, m_s$), which define its energy, shape of its orbital, orientation in space, and spin.
  • Principal Quantum Number ($n$): Defines the principal energy level (shell) and primarily determines the electron's energy and average distance from the nucleus ($n = 1, 2, 3, \dots$).
  • Angular Momentum (Azimuthal) Quantum Number ($l$): Defines the shape of the orbital (subshell) and ranges from $0$ to $n-1$.
    • $l=0$ corresponds to s-orbitals (spherical)
    • $l=1$ corresponds to p-orbitals (dumbbell-shaped)
    • $l=2$ corresponds to d-orbitals (complex shapes)
    • $l=3$ corresponds to f-orbitals (even more complex shapes)
  • Magnetic Quantum Number ($m_l$): Defines the orientation of the orbital in space and ranges from $-l$ to $+l$, including 0. For example, for $l=1$ (p-orbitals), $m_l$ can be $-1, 0, +1$, representing the $p_x, p_y, p_z$ orbitals.
  • Spin Quantum Number ($m_s$): Describes the intrinsic angular momentum (spin) of an electron, with values of $+1/2$ or $-1/2$.