For , take atomic masses , , harmonic frequency , and dipole-function slope at , ( ).…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Deriving the Spectrum, Ch Diatomic rotation-vibration spectra and nuclear spin statistics

Problem

For H79Br\mathrm{H}^{79}\mathrm{Br}, take atomic masses mH=1.008 um_{\rm H} = 1.008\,\mathrm{u}, mBr=78.918 um_{\rm Br} = 78.918\,\mathrm{u}, harmonic frequency ωe=2649.67 cm−1\omega_e = 2649.67\,\mathrm{cm^{-1}}, and dipole-function slope at ReR_e, d′=1.80 D A˚−1d' = 1.80\,\mathrm{D\,\mathring{A}^{-1}} (1 D=3.33564×10−30 C m1\,\mathrm{D} = 3.33564\times10^{-30}\,\mathrm{C\,m}). Its permanent dipole moment is d(Re)=0.827 Dd(R_e) = 0.827\,\mathrm{D}. ((a)) Find the reduced mass μ\mu. ((b)) Compute the fundamental's transition dipole moment ⟨1∣d∣0⟩=d′ℏ/2μω\langle1|d|0\rangle = d'\sqrt{\hbar/2\mu\omega}, in debye. ((c)) State briefly whether this result shows the permanent dipole or the slope d′d' controls the fundamental's strength.

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