  The numerical Monte-Carlo simulations of Cu-K$\alpha$ and Cu-K$\beta$
fluorescence lines induced by monoenergetic Am-241 radiation in copper have
been presented. The simulations included modeling the K$\beta$/K$\alpha$
intensity ratios for various thicknesses of copper. The results obtained using
the FLUKA code were compared to available experimental and theoretical values.
A clear relationship was observed between the simulated K$\beta$/K$\alpha$
intensity ratios and the sample thickness: as the thickness increased, the
K$\beta$/K$\alpha$ ratio also increased until it reached saturation.
