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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?

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

1 Answer 1

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This is an example of terminology which should be taken with a grain of salt.

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 $e = \pu{1.602176634E−19 C}).$

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