We have obtained membership probabilities of stars within a field of from the centre of the open cluster alpha Persei using proper motions and photometry from the PPMXL and Wide-field Infrared Survey Explorer catalogues. We have identified 810 possible stellar members of alpha Persei. We derived the global and radial present-day mass function (MF) of the cluster and found that they are well matched by two-stage power-law relations with different slopes at different radii. The global MF of alpha Persei shows a turnover at m=0.62M_{sun}_ with low- and high-mass slopes of {alpha}_low_=0.50+/-0.09 (0.1<m/M_{sun}_<0.62) and {alpha}_high_=2.32+/-0.14 (0.62<=m/M_{sun}_<4.68), respectively. The high-mass slope of the cluster increases from 2.01 inside 110 to 2.63 outside 22, whereas the mean stellar mass decreases from 0.95 to 0.57M_{sun}_ in the same regions, signifying clear evidence of mass segregation in the cluster. From an examination of the high-quality colour-magnitude data of the cluster and performing a series of Monte Carlo simulations, we obtained a binary fraction of fbin=34+/-12 per cent for stars with 0.70<m/M_{sun}_<4.68. This is significantly larger than the observed binary fraction, indicating that this open cluster contains a large population of unresolved binaries. Finally, we corrected the MF slopes for the effect of unresolved binaries and found low- and high-mass slopes of {alpha}_low_=0.89+/-0.11 and {alpha}_high_=2.37+/-0.09 and a total cluster mass of 352M_{sun}_ for alpha Persei.