When an electron moves from the ground state to the excited state:
a) it emits energy and moves farther from the nucleus.
b) emits energy and moves closer to the nucleus.
c) absorbs energy and moves closer to the nucleus.
d) absorbs energy and moves farther from the nucleus.

d) absorbs energy and moves farther from the nucleus.

Explanation:

Absorption is the phenomenon whereby the energy of a photon is taken by a particle, like an atom, whose valence electrons take this energy, moving from a lower level (ground state) to a higher level (excited state) of electronic energy, moving away from the atomic nucleus.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.