Magnetic Kinetic Inductance Detectors (MKIDs) are very good radiation detectors which are even capable of single photon detection in the near-infra red and higher frequency range. MKIDs are currently used to detect exoplanets and the goal is to also retrieve information of the atmosphere of exoplanets. However, MKIDs don’t have the photon absorption efficiency and resolving power to do this yet. In this thesis we look at the single photon pulses of a new superconducting material, beta phased tantalum (β-Ta), since this material shows promising properties for MKIDs. The single photon pulse shapes of this material are not yet fully understood. Therefore we will create models for the quasiparticle dynamics in β-ta to try and further our understanding of the single photon pulses in this material. From the Rothwarf-Taylor equations we derive multiple models. These are then tested on the data. We first try the double exponential model which does not work. Then we look at the 1/t model and this model does seem to work better. We propose a different response time of the system. Fitting a new response time we get a very good fit to the single photon pulses. The main hypothesis is that there is an extra relaxation time for the quasiparticles as they need to distribute themselves throughout the superconductor. We see that the fitted response time is wavelength dependent which would support the hypothesis. We conclude that the 1/t model with an adjusted response time explains the single photon pule shapes the best.