The high-temperature contribution of vibrational modes to the molar heat capacity of a solid at constant volume is R for each mode of vibrational motion. Hence, because each atom can vibrate in three dimensions, for a monatomic solid, the molar heat capacity at constant volume is approximately 3R.

(a) The specific heat capacity of a certain monatomic solid is 0.392 J · K^–1 · g^–1. The chloride of this element (XCl₂) is 52.7% chlorine by mass. Identify the element.

(b) This element crystallizes in a face-centered cubic unit cell and its atomic radius is 128 pm. What is the density of this solid?