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Question 4: Diatomic molecules - HCl as harmonic oscillator (i) Explain how band heads in the highly resolved spectrum of an electronic transition in a diatomic molecule can be formed. [3 marks] The energy difference between the lowest and next higher vibrational state in hydrogen chloride, HCl, is 0.354 eV. Its moment of inertia is 2.66x10-47 kg m². Assume HCl to be a harmonic oscillator (mú= 1.67 x 10-27 kg, mcı= 5.81x10-26 kg). (ii) (iii) Calculate the equilibrium separation, Re, of the two nuclei. Calculate the zero-point energy, Eo, of HCl. [1 mark] [1 mark] m (iv) Calculate the expectation value of the vibrational amplitude, (R2), in the ground state (R =distance from internuclear equilibrium separation Re between H and CI). [5 marks]