Topic 1 - Quantization of Energy: Waves and Particles

Tera (T)

10¹²

Giga (G)

10⁹

Mega (M)

10⁶

Kilo (K)

10³

Deci (d)

10^-1

Centi (c)

10^-2

Milli (m)

10^-3

Micro (μ)

10^-6

Nano (n)

10^-9

Classical Mechanics

Motion described as particles (Newton) or waves (Maxwell)

Quantum Mechanics

Objects like electrons or light can show both particle-like and wave-like behaviour

Classical Mechanics - Particles

• Governed by Newton’s equations of motion.

• Described using momentum, energy, forces, torques, etc.

• Have mass - (Exception: There are massless quantum mechanical objects that can have particle-like behavior (e.g: photon — a quantised packet of light energy).

Classical Mechanics - Waves

• Governed by Maxwell’s theories

• Carries energy through different medias: Water waves, sound waves, vibrating strings.

• Three Key Properties 

  • Wavelength (λ) — distance between crests/troughs; unit: m.

  • Frequency (f or ν) — waves passing a point per second; unit: Hz (s⁻¹).

  • Speed (s) — waves propagate at a speed that depends on the medium; unit: m s⁻¹.

Observable Properties of Particles

1. Has weight (only for classical mechanics).

2. Momentum Transfer: When two particles collide, they can change the speed of the other by exchanging momentum.

Tip

Before using the wave equation, make sure the units are correct

Electromagnetic (EM) Waves

• Includes light, X-rays, etc.

• Consist of oscillating electric and magnetic fields at right angles.

• Travel at the speed of light

Speed of Light

c = 2.998 × 10⁸ m s⁻¹

Wave Equation

c = λν

Torque

Angular force that causes an object to rotate about an axis

Momentum

Quantity of motion that an object has

Quantization

Electrons can possess only certain, discrete energy values

Observable Properties of Waves

1. Allows for Direct Measurement — of wavelength or frequency (classical waves).

2. Observable Interference Patterns:

• Waves interact (combine) to create regions of high/low intensity:

  • Sound: loud/soft regions.

  • Water waves: high/low wave regions.

  • Light: bright/dark regions.

• Diffraction is also a wave phenomenon.

Diffraction

Spreading/slight bending of light around obstacles (i.e: edges of an opening).

Regions of the Electromagnetic Spectrum

• Classified by wavelength or frequency.

• Visible light: 380–780 nm.

• Ultraviolet (UV): 10–380 nm.

• Infrared (IR): 780 nm – 1 mm.

Unit Conversions

Between Base Unit and Prefixes Higher/Lower:

1. Identify the prefix and its power of 10

2. Write the conversion as a ratio: 1 unit of the prefix = Amount in base units (power of 10)

3. Multiply and cancel units: To cancel, ensure the unit to be cancelled is the denominator

Between Prefixes: Prefix A → Prefix B

1. Identify each prefix and their powers of 10

2. Apply the formula: Value x 10^(Power of A - Power of B)

Photon

Massless, chargeless particle with a discrete energy based upon its frequency