Edit: Karsten added a description of reduced mass:
"It is a quantity which allows the two-body problem to be solved as if it were a one-body problem."
I do not really have a strong Physics background (my highest level is undergraduate level General Physics).
The solution of a problem from Chapter 1 of McQuarrie's Quantum Chemistry, 2nd edition, involves the concept of reduced mass, supposedly because of the phrase singly ionized.
1-34. Using the Bohr theory, calculate the ionization energy (in electron volts and in kJ·mol^(- 1)) of singly ionized helium.
I struggle to understand why sometimes the concept of reduced mass is used, especially after a quick read of a part from Chapter 8A from Atkins' Physical Chemistry, 11th edition page 305:
In all except the most precise work, the reduced mass can be replaced by me.
Can somebody give me an explanation on this matter? Also, in which cases do we not use the reduced mass concept?