Chem 202 - Webtext 2.6

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8/22/11 - 9/9/11 The Quantum World Spectroscopy: photons

Albert Einstein's equation relating mass and energy

E² = m²c⁴ + p²c²

The equation is so often turned into E=mc² because for a massed particle, the momentum is so small that the p²c² term is negligible.

Photons

Light energy comes in small packets of well-defined energy called photons.

Photons vs. Electrons

Photons are electrically neutral, have no mass, and have a spin of 1, not ½.

Photons and the Pauli exclusion principle

Photons do not obey the Pauli exclusion principle; they are gregarious particles.

Energy for a free particle

Energy = mass-energy + kinetic energy.

For a non-free particle, add the potential energy (i.e. the p²c² term).

Energy of a photon

A photon is massless, so its energy is given by

E = pc

p = h / λ

A Fourier principle that holds as a special case for freely moving particles such as photons or electrons not stuck in a box; hence, the wavelength of the particle replaces the length of the box.

Waves and quantum particles

The Heisenberg priciple, with its Fourier-conjugate relationship between momentum and distance, imparts on quantum particles properties usually reserved for waves.

Planck's Law

E = hν

The energy of a photon is linearly proportional to its frequency.

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