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Energetic electrons trapped in the radiation belts undergo bounce motion about the geomagnetic equator. The behaviors of the trajectories of these electrons interacting with a large amplitude whistler wave are explored, with the electron energy and wave amplitude as variable parameters. A surface of section technique is used to examine the chaoticity of the system graphically. The wave amplitude required causing an electron trajectory to become chaotic decreases with increasing electron energy. Once the trajectory of an electron becomes chaotic, it can wander into the loss cone and subsequently precipitates into the ionosphere and/or the upper atmosphere. This chaotic scattering process requires a threshold field for the commencement of chaotic behavior in the electron trajectories. Therefore, a loss-cone negative mass instability process to amplify whistler waves by electrons in the bulk of the energy distribution is also studied. The numerical results show that the injected whistler waves can be amplified by more than 20 dB, agreeing with the experimental results. This amplification process reduces considerably the required field intensity of injected whistler wave for the purpose of precipitating those tail electrons in the megaelectronvolt range.