Origins Page 53

• Energy: Determined by frequency, expressed by the equation E = hf, where h is Planck’s constant.

Explanation for E = hf

The relationship E = hf is one of the most important equations in quantum physics.  It defines how the energy (E) of a photon — the fundamental particle of light — depends directly on its frequency (f).  The constant of proportionality, Planck’s constant (h = 6.626 × 10^-34 joule-seconds), is an extremely small value that sets the scale of quantum effects and governs how energy is quantized in light.

In simple terms, this means that higher-frequency radiation, such as ultraviolet or X-rays, carries more energetic photons capable of causing greater effects, while lower-frequency radiation, such as infrared or radio waves, carries less energetic photons.

This relationship explains why ultraviolet light can cause sunburn while visible light cannot — its photons have greater energy due to their higher frequency and stronger ability to penetrate our skin.

Thus, E = hf reveals the quantized nature of light, showing that electromagnetic energy is not continuous but delivered in discrete packets — photons — each carrying an exact amount of energy determined by its frequency.

Types of Photons

• Visible Light: The photons that make up the sunlight we see, with varying frequencies correspon­ding to different colors.
• Other Radiation: Includes infrared photons (heat), ultraviolet photons (which can cause sunburn), and higher-energy photons like X-rays and gamma rays.

Wave–Particle Duality

• Wave Behavior: A photon can spread out like a wave.  This is seen in phenomena such as diffraction (light bending around corners) and interference (light waves combining, creating pat­terns of bright and dark fringes).  It is described by wave properties like wavelength (λ) and frequency (ν).
• Particle Behavior: When measured, the photon appears as a discrete particle — a single quantum of light. This particle-like nature is demonstrated by the photoelectric effect, where light striking a metal surface ejects electrons, an effect only explained by particle theory. The energy (E) of this particle is directly proportional to the wave’s frequency, as described by the Planck-Einstein relation: E = hν, where h is Planck's constant.