Answer
Bohr model cannot be applied for the neutral $He$ atom since it has 2 electrons. There are also interactions between the electrons themselves, which Bohr model is not yet designed to account for.
Work Step by Step
The neutral $He$ atom has 2 electron surrounding the nucleus. Losing 1 electron, the atom becomes the $He^+$ ion.
That means the $He^+$ ion has only 1 electron, so the Bohr model can be applied.
Bohr model cannot be applied for the neutral $He$ atom since it has 2 electrons. The reason is that Bohr model is only concerned with the interaction between 1 electron and its nucleus. When there are 2 or more electrons in the atom, there are also interactions between the electrons themselves, which dramatically change the way electrons behave in an atom.
