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Resonance scattering techniques are often used to study the properties of atoms and molecules. The Birmingham Solar Oscillations Network (BiSON) makes use of Resonance Scattering Spectroscopy by applying the known properties of potassium vapour to achieve ultra-precise Doppler velocity observations of oscillations of the Sun. We present a model of the resonance scattering properties of potassium vapour which can be used to determine the ideal operating vapour temperature and detector parameters within a spectrophotometer. The model is validated against a typical BiSON vapour cell using a tunable diode laser, where the model is fitted to observed absorption profiles at a range of temperatures. Finally we demonstrate using the model to determine the effects of varying scattering detector aperture size, and vapour temperature, and again validate against observed scattering profiles. Such information is essential when designing the next generation of BiSON spectrophotometers (BiSON:NG), where the aim is to make use of off-the-shelf components to simplify and miniaturise the instrumentation as much as practical.