Wave Nature of Matter & Light; Uncertainty & Microscopy

Vocabulary flashcards covering wave-particle duality, photon energy, de Broglie wavelength, microscopy resolution, and the uncertainty principle.

Wave-particle duality

The concept that matter and energy exhibit both wave-like and particle-like properties.

Frequency (ν)

The number of wavelengths passing a point per second; unit is hertz (Hz, s^-1).

Wavelength (λ)

The distance between successive points of identical phase in a wave (e.g., crest to crest).

Speed of light (c)

The universal constant ~3.00 × 10^8 m/s in vacuum; relates ν and λ via ν = c/λ.

Planck’s constant (h)

A fundamental constant used to relate energy to frequency: E = hν (≈ 6.626 × 10^-34 J·s).

Photon energy (E = hν)

Energy carried by a single photon, proportional to its frequency.

Photon energy using wavelength (E = hc/λ)

An equivalent expression for photon energy using wavelength instead of frequency.

Avogadro’s number (N_A)

6.022 × 10^23; number of particles per mole; used to convert per-photon energy to per-mole energy.

Energy of a mole of photons

Energy of one mole of photons = Eperphoton × N_A.

de Broglie wavelength (λ = h/(mv))

Wavelength associated with a moving object of mass m and speed v; demonstrates the wave nature of matter.

de Broglie wavelength (electron example)

For electrons at 1.9 × 10^6 m/s, the wavelength is about 3.83 × 10^-10 m, illustrating tiny matter waves.

Resolution

The smallest distance at which two points can be distinguished; improves with shorter wavelength.

Light microscope limit of resolution

Limited by the wavelength of light, roughly ~200 nm, restricting detail achievable with optical optics.

Electron microscope

A microscope that uses electrons instead of light, achieving much higher resolution due to their much shorter wavelengths.

Heisenberg’s Uncertainty Principle

Some pairs of properties (e.g., position and momentum) cannot be known exactly at the same time.

Uncertainty principle (mathematical form)

Δx × Δp ≥ h/(4π); expresses the fundamental limit on simultaneous precision of position and momentum.

Single-slit experiment

Demonstrates diffraction and momentum uncertainty; narrowing the slit increases positional certainty but broadens momentum uncertainty.

Picometer (pm)

Unit of length equal to 10^-12 meters.

Nanometer (nm)

Unit of length equal to 10^-9 meters.

SI prefixes (kilo, mega)

Common prefixes: kilo = 10^3, mega = 10^6; used to scale units in scientific notation.