The radiolabelled monoclonal antibody anti-CD20 has the property of binding to the CD20 antigen expressed on the cell surface of B-lymphocytes, thus making it a useful tool in the treatment of non-Hodgkin's lymphoma. In this work, the event-by-event Monte Carlo code NOREC is used to calculate the single-event distribution function f(1)(z) in the cell nucleus using the beta spectra of the (188)Re and (131)I radionuclides. The simulated geometry consists of two concentric spheres representing the nucleus and the cell surface embedded in a semi-infinite water medium. An isotropic point source was placed on the cell surface to simulate the binding of the anti-CD20 labelled with either (188)Re or (131)I. The simulations were carried out for two combinations of cell surface and nucleus radii. A method was devised that allows one to calculate the contribution of betas of energy greater than 1 MeV, which cannot be simulated by the NOREC code, to the single-event distribution function. It is shown that disregarding this contribution leads to an overestimation of the frequency-mean specific energy of the order of 9-12%. In general, the antibody radiolabelled with (131)I produces single-event distribution functions that yield higher frequency-mean specific energies.