We study the impulsively generated non-linear Alfvén waves in the solar atmosphere and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfvén waves in the solar atmosphere model of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfvén waves at different heights of the model atmosphere and estimate its contribution to the unresolved non-thermal motions caused by the waves. We find that the pulse-driven non-linear Alfvén waves with the amplitude Av = 50 km s- 1 are the most likely candidates for the non-thermal broadening of Si viii λ1445.75 Å line profiles in the polar coronal hole as reported by Banerjee et al. We also demonstrate that the Alfvén waves driven by comparatively smaller velocity pulse with amplitude Av = 25 km s- 1 may contribute to the spectral line width of the same line at various heights in coronal hole broadening. We conclude that the non-linear Alfvén waves excited impulsively in the lower solar atmosphere may be responsible for the observed spectral line broadening in polar coronal holes. This is an important result as it allows us to conclude that such large amplitude and pulse-driven Alfvén waves may indeed exist in solar coronal holes. The existence of these waves may impart the required momentum to accelerate the solar wind.