Light as a Particle
Light can be thought of as consisting of photons, “packets” of energy, which are
quantized, and have energies given by the following equation:
E = hf = h λ
E (in eV) = λ(¿nm)
In many modern sources of light, photons of light are produced by electrons making
energy level transitions.
Electrons can also make transitions between energy levels in atoms, as well as
molecules we model as “particles in a box”. If you have a transition between E and E 2 1
the photon will not have an energy equal to E or 1 , bu2 rather the difference between
the energy levels:
E transitionn2-n1or n1, 2 …
Energy Transitions – The Hydrogen Atom
Electrons in atoms are constrained to be near the nucleus. This constraint causes them
to exist in certain quantized energy states.
Passing a current through a gas in a tube causes electrons to jump to higher energy
states then fall back down to the lowest energy state, the ground state. As they do so,
they emit a photon with an energy equivalent to the difference in energy between the two
Energy levels is different for each element → each element has a characteristic
Energy levels for hydrogen follow the equation:
E n - 8ε h n2 2 = -13.6 eV ( n2 ) for n = 1, 2, 3…
All of these energy levels are negative. E = 0 eV corresponds to a free electron; these
are bound states of the electron.
Energy Transitions – Particle in a Box
Particles have a wave nature. If you trap a particle in a “box,” the wave will only have
certain states available to it – quantized energy states.
For a particle in a one-dimensional box of length L, these energy levels are given by: h2
E n1 2 n1