For a given type of wave in a given medium, the wavelength
l and the frequency n
can be related to the speed of propagation of the wave. l n = c A device that separates light by its frequency is said to 'disperse' the light.
Prisms and raindrops disperse light by refraction, gratings and holograms by
refraction.
E = h n When light strikes matter, and in particular a molecule, the entire energy of the
photon must be absorbed or emitted. Thus the color of the light that interacts with a
particular piece of matter tells you about the change in energy that is possible in
that matter,
If Light has properties of a particle, surely particles have properties of a wave.
DeBroglie showed that this was in fact the case, in the first equation that has both
wave and particle like properties related:
p = h / l When one confines a wave to a particular region of space, the edges of the
containment place a constraint on the wavelength due to 'boundary conditions'. This
is how you play different notes on the same guitar string by moving the position in
which you make the wave amplitude zero, i.e. where your finger touches the fret.
If electrons are waves, then the wavelenght of the electron must 'fit' into any
orbit that it makes around the nucleus in an atom. All orbits that do not have
the electrons wavelenght 'fit' are not possible, because wave interference will
rapidly destroy the wave amplitude and the electron wouldn't exist anymore.
This 'interference' effect leads to dicrete (quantized) energy levels and the
discrete 'line' spectrum of the hydrogen atom:
This cloud is only spherical for the lowests energy level of the atom. As the
energy of the electron in the atom increases, its wavelength decreases, and the number
of times the wave amplitude crosses zero per orbit increases. These zero crossings are
called nodes. The number of nodes is related to the frequency of the wave and
therefore its energy. The number of nodes determines the energy. The Principle quantum number n is
equal to the number of nodes plus 1, i.e. nodes= n-1. For a hydrogen atom,
the energy it takes to make a radial node is
equal to the the energy it takes to make an angular node.
For higher n, you can have a greater numbers of nodes. For n>=3,
you can have 2 angular nodes, and these are called d orbitals
Here are some more pictures of the atomic
orbital shapes
In short, the energy of the atom is determined by the number of nodes (n-1). PJ Brucat // University of Florida
For Light (electromagnetic waves) the speed of
propagation is the speed of light: 3 x 108 m/s.
Light is just one portion (one range of frequencies) of the EM spectrum
The frequency of the transitions between the energy levels should be given by
The energy patterns of atoms give the elements their characteristic 'flame' colors
We know, too, that Sodium is yellow (Streetlights) and Neon is red
(Fluorescent Signs)...
The wave nature of the electron is what makes atoms have the properties that they do.
It explains the colors of the atoms and also their size. It also means that we cannot
think about the electron in an atom as a little ball whirling about the nucleus,
but a cloud of probability that is smeared out over the orbit.
The greater number of nodes, the greater the energy.
The
lowest level of the H atom has no (zero) nodes, the next higher level has 1 node, but
that node can either be an angular node or a radial node. If it is an angular node,
then you have a 2p orbital
If you have a radial node, then you have a 2s orbital (3s shown also)
The number of angular nodes is labelled by a letter
The number of radial nodes is the total number of nodes minus the number of angular
nodes.