Atomic Models

Full Notes:

Models to describe atomic structure have changed over time, based on experimental data and observations.

2.2.1 Thomson’s Model of Atom (1898)

Also known as the plum pudding model, Thomson’s Model was the first structured attempt to describe the atom after the discovery of electrons.

Main Points:

• Atom is a uniformly positively charged sphere.
• Electrons are embedded in this sphere like “plums” in a pudding.
• The total positive charge balances the negative charge, making the atom neutral.

Limitation:

Could not explain the results of the alpha scattering experiment by Rutherford. No concept of a nucleus or structured electron motion.

2.2.2 Rutherford’s Nuclear Model of Atom (1911)

Rutherford’s nuclear model was based on his famous alpha particle scattering experiment.

Experiment:

• A thin gold foil was bombarded with alpha particles (He²⁺).
• Most alpha particles passed through undeflected.
• A small number were deflected at small angles.
• A very few were deflected back sharply.

Conclusions:

• Atom is mostly empty space.
• A dense, positively charged nucleus is present at the center.
• Electrons revolve around the nucleus in circular orbits.
• Nucleus contains nearly all the mass of the atom.

Atomic size scale:

• Radius of atom ≈ 1 × 10⁻¹⁰ m
• Radius of nucleus ≈ 1 × 10⁻¹⁵ m
• Therefore, atom is about 100,000 times larger than the nucleus.

2.2.3 Atomic Number and Mass Number

Atomic Number (Z):

• Number of protons in the nucleus.
• Also equals the number of electrons in a neutral atom.
• Determines the identity of the element.

Mass Number (A):

• Total number of protons + neutrons.
• Also called nucleons.

Relation: A = Z + number of neutrons

2.2.4 Isobars and Isotopes

Isobars:
Atoms with the same mass number (A) but different atomic numbers (Z). They are different elements with the same total number of nucleons.

Isotopes:
Atoms of the same element with the same atomic number (Z) but different mass numbers (A). Chemically similar but differ in physical properties like mass and stability.

2.2.5 Drawbacks of Rutherford’s Model

While Rutherford’s model successfully introduced the concept of a dense, positively charged nucleus, it failed to explain the stability of the atom.

1. Comparison with the Solar System

Rutherford compared the atom to the solar system:

• The nucleus is like the sun.
• Electrons revolve around the nucleus like planets around the sun.

In classical mechanics, the force responsible for keeping planets in orbit is gravitational force, given by F = G m₁ m₂ / r². This theory accurately explains planetary orbits.

2. Coulomb Force in Rutherford’s Atom

In an atom, the attractive force between the negatively charged electron and the positively charged nucleus is given by Coulomb’s law, similar in form to gravitation: F = k q₁ q₂ / r². Because of this resemblance, it seemed logical to assume electrons could orbit the nucleus like planets.

3. Problem of Accelerated Motion

Here is where the flaw appears:

An electron in circular motion is continuously changing direction, i.e., accelerating. According to Maxwell’s electromagnetic theory, an accelerating charge must emit radiation. Hence, an orbiting electron should lose energy continuously and spiral into the nucleus.

4. The 10⁻⁸ Seconds Collapse Problem

Calculations based on classical physics predict that such an electron would collapse into the nucleus in about 10⁻⁸ s. This implies atoms should not be stable — contradicting observation.

5. Inability to Explain Atomic Spectra

Rutherford’s model predicts continuous radiation as electrons spiral inward, but experiments show discrete line spectra of specific wavelengths. This indicates quantized energy levels, absent in Rutherford’s model.

Conclusion:

The Rutherford model failed because it could not explain atomic stability or the discrete spectra of atoms. These limitations paved the way for Bohr’s model, which introduced quantum concepts to describe atomic structure.

Summary

• Thomson proposed a uniform positive sphere with embedded electrons (plum pudding).
• Rutherford established the nuclear atom with a dense, positive nucleus and orbiting electrons.
• Atomic number Z counts protons; mass number A counts total nucleons.
• Isotopes share Z but differ in A; isobars share A but differ in Z.
• Rutherford’s model fails for stability and spectral lines, motivating quantum models.