Atomic Theory

Overview

Atomic theory describes the nature and structure of matter at the atomic level. It has evolved from ancient philosophical ideas to the modern quantum mechanical model.

Historical Development

Scientist	Year	Model	Key Contribution
Dalton	1803	Solid Sphere	Atoms are indivisible; elements have unique atoms
Thomson	1897	Plum Pudding	Discovery of electrons; negative charges in positive "pudding"
Rutherford	1911	Nuclear	Dense positive nucleus with orbiting electrons
Bohr	1913	Planetary	Electrons in fixed energy levels (orbits)
Schrödinger	1926	Quantum Mechanical	Electrons exist in probability clouds (orbitals)

Dalton's Atomic Theory

1. All matter is made of indivisible atoms
2. Atoms of the same element are identical in mass and properties
3. Atoms of different elements have different masses and properties
4. Atoms combine in simple whole-number ratios to form compounds
5. Atoms cannot be created or destroyed in chemical reactions

Subatomic Particles

Particle	Symbol	Charge	Mass (amu)	Location
Proton	p⁺	+1	1.0073	Nucleus
Neutron	n⁰	0	1.0087	Nucleus
Electron	e⁻	-1	0.00055	Orbitals

Key Definitions

• Atomic Number (Z): Number of protons in the nucleus
• Mass Number (A): Total number of protons + neutrons
• Isotopes: Atoms with the same Z but different numbers of neutrons

$$\text{Mass Number (A)} = \text{Protons} + \text{Neutrons}$$ $$\text{Number of Neutrons} = A - Z$$

Atomic Mass

The weighted average of all naturally occurring isotopes:

$$\text{Atomic Mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$$

Example

Chlorine has two isotopes:

• ³⁵Cl (75.77%) with mass 34.97 amu
• ³⁷Cl (24.23%) with mass 36.97 amu

$$\text{Atomic mass} = (34.97 \times 0.7577) + (36.97 \times 0.2423)$$ $$= 26.50 + 8.96 = 35.46 \text{ amu}$$

Modern Atomic Model

The quantum mechanical model describes electrons as:

• Existing in orbitals (probability distributions)
• Having both wave and particle properties
• Described by four quantum numbers
• Following the Heisenberg Uncertainty Principle

Key Equations

de Broglie Wavelength

$$\lambda = \frac{h}{mv}$$

Where:

• $\lambda$ = wavelength (m)
• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)
• $m$ = mass (kg)
• $v$ = velocity (m/s)

Heisenberg Uncertainty Principle

$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$

The position and momentum of a particle cannot both be known precisely.