Dual Nature of Light

Vocabulary flashcards covering the key concepts, formulas, equations, and definitions regarding the Dual Nature of Light from the provided lecture notes.

Matter-Wave (de-Broglie Hypothesis)

The hypothesis stating that a moving particle displays wave-like properties under specific conditions, and that matter and radiant energy possess symmetry.

Effective Mass of a Photon ($m$)

The relativistic mass equivalent of a photon given by $m = \frac{E}{c^2} = \frac{h\nu}{c^2} = \frac{h}{c\beta}$, where $m \times \frac{1}{\beta}$ (the mass of a violet photon is greater than that of a red photon).

Linear Momentum of Photons ($P$)

The momentum associated with a photon, defined as $P = mc = \frac{h}{\beta}$.

Intensity of Light ($I$)

The energy incident per unit area per unit time, given by $I = \frac{E}{At} = \frac{P}{A} = \frac{N h\nu}{At}$.

Work Function (\threshold)

The minimum amount of energy required to eject an electron from a metal surface.

Thermionic Emission

The ejection of electrons from a metal surface caused by thermal energy (heat).

Field Emission

The emission of electrons from a metal surface induced by a strong external electric field.

Stopping Potential ($V_0$)

The magnitude of the minimum negative potential applied at the anode relative to the cathode at which the photoelectric current ($I_p$) drops to zero.

Quantum Efficiency ($x$)

The ratio of emitted electrons to incident photons, given in the text as $x = \frac{n_e}{n_{ph}} = 5 \times 10^{-24}$.

de-Broglie Wavelength of an Electron ($\beta_{e^-}$)

The de-Broglie wavelength associated with an electron accelerated through potential difference $V$, expressed as $\beta_{e^-} = \frac{h}{P} = \frac{h}{\beta 2km} = \frac{h}{\beta 2qVm} = \beta \frac{150}{V}\text{\thinspace \text{\text{\r{A}}}}$ in volts.

de-Broglie Wavelength of Gas Molecule ($\beta_{gas}$)

The thermal de-Broglie wavelength of a gas molecule defined by $\beta_{gas} = \frac{h}{\beta 3m k_B T}$, based on average kinetic energy $K.E. = \frac{3}{2} k_B T$.

Einstein's Photoelectric Equation

The fundamental energy relationship for photoelectric emission: E = \threshold + (K.E.)_{max}, or $h\nu = h\nu_0 + e V_0$.

Threshold Frequency ($\nu_0$)

The minimum frequency of incident light required to produce photoelectric emission from a given metal surface.

Photoelectric Current ($I_p$)

The electric current produced by photoelectrons, calculated as $I_p = \frac{Q}{t} = n e e = 1.6 \times 10^{-19} n_e$.