Page 226 - Instant notes

G3
QUANTIZATION OF ENERGY AND
PARTICLE-WAVE DUALITY

Key Notes
Classical physics assumes that particles move along precisely
defined trajectories and can possess any amount of energy. The
failure of classical physics to account for observed phenomena
such as black body emission and the photoelectric effect was
resolved by the postulates of quantization and particle wave-
duality and showed that classical mechanics was an approximate
description of a more fundamental quantum mechanics.
Quantization is the confinement of a property (such as energy,
momentum or position in space) to a set of discrete values, called
quanta.
The Planck constant, h, is the constant of proportionality between
a quantum of energy, E, and the frequency, v, of the
corresponding photon of electromagnetic radiation, E=hv. Its
value is 6.626×10 −34 J s.
The classical physics interpretation of the power emitted by a
black body assumes that electromagnetic oscillators can oscillate
at all frequencies. This leads to the ultraviolet catastrophe in
which black body emission is predicted to increase to infinity at
high radiation frequency. The postulates that energy is quantized
according to frequency, and that oscillators can only be excited
by energy equal to the quanta, resolves the problem.
The photoelectric effect is the emission of electrons from a
surface irradiated by ultraviolet light. No electrons are emitted
unless the radiation frequency exceeds a threshold value
characteristic of the surface. The kinetic energy of the electrons
varies linearly with the frequency of the radiation and is
independent of the intensity of the radiation. The effect is
evidence that radiation is quantized into particles (photons) with
energy proportional to frequency.
Light passing through two closely spaced narrow slits produces a
diffraction pattern of alternating dark and light fringes, readily
interpreted in terms of constructive and destructive interference
of wave fronts passing through the slits. The observation that
particles produce the same effect is evidence of particle-wave
duality.
The de Broglie equation summarizes the relationship between
particle momentum, p(=mυ) and wavelength, λ, in the particle-
wave duality interpretation of matter and radiation, p=h/λ.