According to the Bohr model, the energy of an electron in a hydrogen-like species (single electron system) is proportional to the square of the atomic number ($Z$). The ionization energy (IE) is given by $IE = 13.6 \times \frac{Z^2}{n^2}$ eV. For the ground state ($n=1$):

1. For Hydrogen ($Z=1$): $IE = 13.6 \times 1^2 = 13.6$ eV.
2. For Helium ion ($He^+$, $Z=2$): $IE = 13.6 \times 2^2 = 13.6 \times 4 = 54.4$ eV. (Note: While the question says 'helium atom', the answer 54.4 eV corresponds to the singly ionized helium ion $He^+$, which is a hydrogen-like species applicable to Bohr's theory. The ionization energy of neutral Helium is \approx 24.6 eV).