ch 301 lecture 1

Rutherford Model

Atoms visualized as planetary systems: a small, dense nucleus with electrons orbiting around it. Classical mechanics failed to explain its stability as electrons should radiate energy and spiral into the nucleus.

Classical Mechanics (failure for atoms)

Explained macroscopic motion well but failed for atoms because charged electrons, when accelerated in circular orbits, would radiate energy, lose energy, and spiral into the nucleus, contradicting observed atomic stability.

Electromagnetic Radiation (EMR)

Light composed of oscillating electric and magnetic fields perpendicular to each other and to the direction of travel, propagating through space at the speed of light (c = 3 \times 10^{8}\ \mathrm{m\,s^{-1}}).

Wavelength (\lambda)

The distance between identical points on successive cycles of a wave (e.g., peak to peak or trough to trough).

Frequency (\nu)

The number of cycles per second, measured in hertz (Hz, s^{-1}).

Amplitude (of a wave)

The height of the wave; relates to brightness/intensity (larger amplitude = brighter; smaller amplitude = dimmer).

Relationship between wavelength and frequency

Expressed as
u = \frac{c}{\lambda} or equivalently, \lambda = \frac{c}{\nu}, where c is the speed of light.

Electromagnetic Spectrum

The full range of all types of electromagnetic radiation, ranked by frequency and wavelength, illustrating their inverse relationship. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Visible Light

The narrow band of the electromagnetic spectrum that the human eye can perceive, remembered via the Roy G. Biv mnemonic (Red, Orange, Yellow, Green, Blue, Indigo, Violet).

Planck’s Constant (h)

A fundamental constant, approximately 6.626 \times 10^{-34}\ \mathrm{J\,s}, that relates the energy of a photon to its frequency.

Photon Energy (E)

The energy carried by a photon, calculated using the formulas E = h\nu or E = \frac{h c}{\lambda}.

Wave-Particle Duality

The concept that light exhibits both wave-like and particle-like properties, explaining phenomena such as interference (wave) and the photoelectric effect (particle).

Photon

A packet or quantum of light that carries energy (E_{\text{photon}} = h\nu = \frac{h c}{\lambda}). Its energy must reach a threshold to cause electron emission in the photoelectric effect.

Work Function (\phi)

The minimum threshold energy required for an electron to be ejected from a metal surface. If the photon energy (E{\text{photon}}) is less than "\phi", no emission occurs. If E{\text{photon}} \ge \phi, the excess energy becomes kinetic energy: K.E. = E_{\text{photon}} - \phi.

Photoelectric Effect

The phenomenon where electrons are ejected from a metal surface when light shines on it, demonstrating the particle nature of light (photons) and the necessity of a threshold energy (work function) for electron emission to occur.