Afrikaans Vowels

Spelling, Time, Numbers, Sounds

Short Vowels

• a: as in "man", "vakansie"
• e: as in "pen", "eksamens"
• o: as in "kop", "bottel"
• u: as in "brug", "kultureel"
• i: as in "dit", "vinnig"

Twin Vowels

• aa: as in "maan", "kaas"
• ee: as in "peer", "kleedkamer"
• oo: as in "koop", "stoomboot"
• uu: as in "vuur", "muurbal"
• ie: as in "siek", "piekniek"
• ê: k as in "sê", "wêreld"
• ë: as in "geëet", "pasiënt"

Double/Long Vowels

• ae: as in "hael", "uraend"
• eu: as in "seun", "reusagtig"
• ou: as in "houd", "skouers"
• oe: as in "boek", "moedeloos"
• ei: as in "klein", "skeidsregter"
• ui: as in "huis", "tuin"
• y: as in "hy", "medisyne"

Triple Vowels

• aai: as in "slaai", "braai"
• eeu: as in "leeu", "eeufees"
• ooi: as in "rooi", "toernooi"
• oei: as in "koei", "groei"

Planck's Constant

• Represented by the symbol h.
• Is a fundamental constant of nature that relates the energy of a photon to its frequency.
• Plays a crucial role in quantum mechanics.
• Currently accepted value: $h = 6.62607015 \times 10^{-34} J \cdot s$

Overview

Definition

• Quantum of action in quantum mechanics.
• Relates the energy (E) of a photon to its frequency (v): $E = h \cdot v$
  • E is the energy of the photon in joules (J).
  • v is the frequency of the photon in hertz (Hz).

Significance

• Quantization of Energy: Implies energy isn't continuous but quantized in discrete packets.
• Quantum Mechanics: Fundamental to understanding quantum phenomena at atomic/subatomic levels.

History

• Introduced in 1900 by Max Planck to explain the black-body radiation spectrum.
• Postulated energy could only be emitted/absorbed in discrete amounts, multiples of $h \cdot v$

Implications and Applications

Black-Body Radiation

• Accurately describes the black-body radiation spectrum, resolving the ultraviolet catastrophe.

Photoelectric Effect

• Einstein used it to explain the photoelectric effect, demonstrating light consists of photons with energy $E = h \cdot v$

Atomic Spectra

• Used in the Rydberg formula to calculate the wavelengths of light emitted by atoms.

Quantum Technologies

• Essential in quantum computing, quantum cryptography and quantum sensors.

Measurement

Experimental Determination

• Determined through:
  • Photoelectric effect experiments
  • Black-body radiation measurements
  • X-ray spectroscopy

CODATA Value

• The Committee on Data for Science and Technology provides accepted values of fundamental physical constants like Planck's constant.

Relationships with Other Constants

Reduced Planck Constant

• Defined as Planck's constant divided by $2\pi$: $\hslash = \frac{h}{2\pi} \approx 1.0545718 \times 10^{-34} J \cdot s$
• More commonly used in quantum mechanics.

Fine-Structure Constant

• Related to Planck's constant (ħ), speed of light (c), and elementary charge (e): $\alpha = \frac{e^2}{4 \pi \varepsilon_0 \hslash c} \approx \frac{1}{137.036}$
• Characterizes the strength of electromagnetic interaction.

Conclusion

• Cornerstone of quantum mechanics, providing the fundamental unit of energy quantization.
• Its discovery revolutionized physics and led to quantum theory.
• Remains vital in theoretical and applied physics, underpinning modern technologies.