Yes, in a classical model of the singly-ionized helium atom, a single electron orbits the nucleus.
Singly ionized helium is an atom that has lost one electrons from its outermost shell. We consider its remaining electron like a hydrogen electron. There is only one difference between a hydrogen atom and a singly ionized helium atom which is the number of protons in the nucleus so the nucleus charge on singly ionized helium is -1.
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