The vibrational levels of ¹³Na¹¹⁷ l lie at the wavenumbery 142.81, 427.31, 710.31, and 991.81 cm⁻¹. Show that they fit the expression (v+1/2) v-(v+1/2)¹ x₂ v, and deduce the force constant, zero-point energy, and dissociation energy of the molecule.
a) 1/2kv² = v - 1/2x₂v
b) k = 2(v-x₂v)/v²
c) E₀ = 1/2kv²
d) D = 1/2kv² - 1/2x₂v²