This work presents an upper bound on the neutrino mass using the emission of $ u_e$ from the neutronization burst of a core collapsing supernova at 10~kpc of distance and a progenitor star of 15~M$_odot$. The calculations were done considering a 34 k
ton Liquid Argon Time Projection Chamber similar to the Far Detector proposal of the Long Baseline Neutrino Experiment (LBNE). We have performed a Monte Carlo simulation for the number of events integrated in 5~ms bins. Our results are $m_ u<2.71$~eV and $0.18~mbox{eV}<m_ u<1.70$~eV, at 95% C.L, assuming normal hierarchy and inverted hierarchy, respectively. We have analysed different configurations for the detector performance resulting in neutrino mass bound of $mathcal{O}(1)$~eV.
