Final answer:
To calculate the electronic polarizability and relative permittivity, additional information and specific physics equations are needed, which are not provided in the details given. The nature of this calculation, in a quantum mechanical context, would also require consideration of the quantum states of the electron in the hydrogen atom.
Step-by-step explanation:
To calculate the electronic polarizability and relative permittivity for hydrogen gas with 9.8 × 10²⁰ atoms/cc and a radius of 0.053 nm, we would typically employ physics concepts such as the polarizability of an atom and the relation between polarizability and permittivity. However, the exact methodology for calculating these values would require additional formulae and constants which are not provided in the information snippet, including the use of Clausius-Mossotti relation or Lorentz-Lorenz equation to relate polarizability and permittivity.
In classical physics, the polarizability α of a hydrogen atom can be thought of as the measure of how much the electron cloud distorts in response to an external electric field. However, additional information such as the dielectric constant of the medium and the intrinsic susceptibility must be known to calculate the relative permittivity.
Without these, a definitive calculation cannot be provided. Considering the quantum mechanical model, the radius given for a quantum state n of 3 for an electron, the polarizability would also be influenced by the quantum mechanical properties of the atom.