# What is the unit of Z effective?

Z effective is the net positive charge experienced by an electron. But what is the unit of this net charge: coulomb (C) or microcoulomb (μC), or something else?

• What is the charge of a magnesium ion? Which units are you using in your answer?
– Karsten
Jul 19, 2020 at 3:16

The term "effective nuclear charge" is often casually symbolized with $$Z_\mathrm{eff}.$$ This is a universally accepted simplification, but you should keep in mind that the effective nuclear charge is, strictly speaking, $$Z_\mathrm{eff}e,$$ where $$e$$ is the elementary charge. Similarly, the full nuclear charge is $$Ze,$$ where $$Z$$ is the atomic number.
So, it would be more appropriate to refer to $$Z_\mathrm{eff}$$ as to effective atomic number since $$Z_\mathrm{eff}$$ is defined as a function of $$Z$$ $$(Z_\mathrm{eff} = f(Z_i)).$$ For example, the common form provided in every introductory physical chemistry textbook is
$$Z_\mathrm{eff} = Z − σ,$$
where $$σ$$ is the shielding constant of the nucleus (empirical dimensionless parameter).
Since $$Z$$ is dimensionless, so is $$Z_\mathrm{eff}.$$ However, effective nuclear charge $$Z_\mathrm{eff}e$$ is not, and can, for instance, be expressed in coulombs (in the SI system $$e = \pu{1.602176634E−19 C}).$$