The relative binding of the extra electron in the arsenic atom that replaces an atom in silicon

Question:

The relative binding of the extra electron in the arsenic atom that replaces an atom in silicon or germanium can be understood from a calculation of the first Bohr orbit of this electron in these materials. Four of arsenic's outer electrons form covalent bonds, so the fifth electron sees a singly charged center of attraction. This model is a modified hydrogen atom. In the Bohr model of the hydrogen atom, the electron moves in free space at a radius a₀ given by

When an electron moves in a crystal, we can approximate the effect of the other atoms by replacing ?₀ with ??₀ and m_e with an effective mass for the electron. For silicon ??is 12 and the effective mass is about 0.2m_e. For germanium ??is 16 and the effective mass is about 0.1m_e. Estimate the Bohr radii for the outer electron as it orbits the impurity arsenic atom in silicon and germanium.