For the hydrogen transition (part of the Balmer complex, )

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Radiative transitions and lifetimes

Problem

For the hydrogen transition 3d→2p3d \to 2p (part of the Balmer α\alpha complex, λ=656.3 nm\lambda = 656.3\,\mathrm{nm}), the measured spontaneous rate is A(3d→2p)=6.47×107 s−1A(3d\to2p) = 6.47\times10^7\,\mathrm{s^{-1}}. ((a)) Use A21=ω3∣d⃗21∣23πϵ0ℏc3A_{21} = \dfrac{\omega^3|\vec d_{21}|^2}{3\pi\epsilon_0\hbar c^3} to find ∣d⃗32∣|\vec d_{32}|, quoting it as a multiple of ea0ea_0. ((b)) Find the partial lifetime 1/A(3d→2p)1/A(3d\to2p) associated with this single channel, in nanoseconds.

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