Atoms have quantized energy levels similar to those of Planck’s oscillators, although the energy levels of an atom are usually not evenly spaced. When an atom makes a transition between states separated in energy by ΔE, energy is emitted in the form of a photon of frequency f = ΔE/h. Although an excited atom can radiate at any time from t = 0 to t = ∞ the average time interval after excitation during which an atom radiates is called the lifetime τ. If τ = 1.0 × 10-8 s, use the uncertainty principle to compute the line width Δf produced by this finite lifetime.

Atoms have quantized energy levels similar to those of Planck’s oscillators, although the energy levels of an atom are usually not evenly spaced. When an atom makes a transition between states separated in energy by ΔE, energy is emitted in the form of a photon of frequency f = ΔE/h. Although an excited atom can radiate at any time from t = 0 to t = ∞ the average time interval after excitation during which an atom radiates is called the lifetime τ. If τ = 1.0 × 10-8 s, use the uncertainty principle to compute the line width Δf produced by this finite lifetime.