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### Given Data: For \( ^1H^{19}F \), the lowest wave number absorption line in its rotational spectrum occurs at: \[ \tilde{\nu}_1 = 41.11 \, \text{cm}^{-1} \] ### Step 1: Understanding Rotational Absorption Lines For a rigid rotor, the energy levels in rotational spectroscopy are given by: \[ E_J = B J (J+1) \] where \( B \) is the rotational constant and \( J \) is the rotational quantum number. The selection rule for rotational transitions is: \[ \Delta J = +1 \] Thus, the wavenumber of the rotational transitions is given by: \[ ________ _______ __________ __________ _______.
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