Q.Why interstitial hydrides have a lower density than the parent metal.

Many d-block and f-block transition metals (such as palladium, titanium, zirconium, vanadium and the lanthanoids) absorb dihydrogen into their crystal lattices, with the small hydrogen atoms occupying interstitial voids between the metal atoms rather than replacing them. Because the overall metallic lattice and metallic bonding are largely retained, these interstitial hydrides keep many metallic properties such as electrical conductivity and lustre, though usually somewhat diminished. A distinctive feature is that their composition is frequently non-stoichiometric — for example $TiH_{1.7}$ or $LaNi_5H_6$ — because the number of hydrogen atoms occupying the available interstitial sites can vary continuously with temperature and hydrogen pressure, unlike a fixed-ratio ionic hydride. Alkali metals, in contrast, are not expected to form this class of non-stoichiometric hydride because their larger atomic size, distinct (ionic rather than interstitial-metallic) bonding mode, and formation of a well-defined $H^-$ ioni …