Principles of Absorption and Fluorescence

Abstract

Consider two non-degenerate levels of an atom (or molecule) with respective energies E ₁ and E ₂ in the presence of radiation of a frequency satisfying the Bohr condition

$$v = \left( {{E_2} - {E_1}} \right)/hv,$$

(1)

where h is Planck's constant, 6.626 × 10_-34 J s. If an atom in the lower energy state |1〉 absorbs a photon of frequency v it may be excited to the upper state |2〉. This process is termed induced absorption or, more generally, simply absorption. The probability per second that an atom will absorb a photon, dP ₁₂/dt, is proportional to the number of photons of energy hv per unit volume, p(v), and is usually expressed as:

$${{d{P_{12}}} \over {dt}} = {B_{12}}\rho \left( v \right),$$

(2)

where the proportionality constant B ₁₂ is the Einstein coefficient of induced absorption (units J^-1 m³ s^-2).