Before revision: From these limits, theoretical expressions for predicting the Young's modulus were devolped,, for ideal extreme-modulus solids, where , , , and are the reduced Planck constant, electron mass, Bohr radius, and mass density of valence electrons .
After revision: From these limits, theoretical expressions for predicting the Young's modulus were devolped,, for ideal extreme-modulus solids, where , , , and are the reduced Planck constant, electron mass, Bohr radius, and the ratio of valence-electronnumber to atomic mass,proton mass, .