The determination of the isotopic ratio of 239Pu and 240Pu by alpha-particle spectrometry is limited due to the small differences in the alpha-particle energies. But taking into account the differences in the L X-ray emission probabilities of the two plutonium isotopes, an additional L X-ray measurement allows the isotopic ratio of 239Pu and 240Pu to be determined. The sensitivity of this method can be improved, as described in this work, by performing the L X-ray measurement in an underground laboratory.