Why do heavier elements have smaller specific heat values. In the periodic table the trend is that as the mass of each element increase's the specific heat tends to go down. This seems to be counter-intuitive because if I am not mistaken as mass increase's the amount of heat that the substance can hold goes up. So why does the specific heat of these elements go down?
The more particles in a system, the more modes of vibration (and rotation), so one gram of $\ce{H2}$ has about $235 \times$ more particles than one gram of U. The heat is "stored" in the motions of the atoms and electrons, until reaching millions of kelvin, at which point dissociation of the nucleus would be significant in specific heat. See these links and  for more information.