Quantum Theory and Wave–Particle Duality - AP Physics 2

Wavelength decreases. Inverse relationship from $c = f\lambda$ at constant speed.

Planck's constant, $h$. Universal quantum constant in energy and wave relations.

Ejection of electrons by light. Light removes electrons from material surfaces.

Use $E = \frac{hc}{\lambda}$. Substitute wavelength into energy-wavelength relationship.

Planck's constant, $h$. Fundamental constant in energy quantization formulas.

Minimum energy needed to remove an electron from a material. Energy threshold for electron emission from surface.

Inversely proportional, $c = f\lambda$. Higher frequency means shorter wavelength for constant speed.

$\lambda = \frac{h}{p}$. Apply de Broglie formula with given momentum value.

$\lambda = \frac{h}{p}$. Apply de Broglie formula with given momentum value.

Inversely proportional, $c = f\lambda$. Higher frequency means shorter wavelength for constant speed.

Wavelength of a particle. Matter wavelength in de Broglie's wave hypothesis.

$\Delta x \Delta p \geq \frac{\hbar}{2}$. Fundamental quantum limit on simultaneous measurements.

$KE = hf - \phi$. Kinetic energy equals incident photon energy minus work function.

$E = \frac{hc}{\lambda}$. Apply energy-wavelength formula with given wavelength value.

$E = hf$. Directly proportional relationship between photon energy and frequency.

Particles exhibit both wave-like and particle-like properties. Fundamental quantum principle describing matter and energy behavior.

Inversely proportional, $\lambda = \frac{h}{p}$. Higher momentum gives shorter wavelength.

Photon energy increases with frequency. Direct proportionality from $E = hf$ relationship.

Planck's constant, $h$. Fundamental constant in energy quantization formulas.

$p = \frac{h}{\lambda}$. Use momentum formula with given wavelength value.

Minimum energy needed to remove an electron from a material. Energy threshold for electron emission from surface.

$\Delta x \Delta p \geq \frac{\hbar}{2}$. Position and momentum cannot both be precisely known simultaneously.

$\lambda = \frac{h}{p}$. Matter wavelength formula using momentum.

Demonstrates wave-particle duality. Shows particles behave as both waves and particles.

Higher energy. Energy directly proportional to frequency via $E = hf$.

$E = hf$. Planck's quantum energy formula for photons.

Wave and particle. Light exhibits both wave and particle characteristics.

Reduced Planck's constant, $\hbar = \frac{h}{2\pi}$. Appears in angular momentum and uncertainty relations.

$\lambda = \frac{h}{p}$. Relates particle wavelength to momentum through Planck's constant.