# 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

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 $$e = \pu{1.602176634E−19 C}).$$

• Thanks a lot.... Plz tell that if my Zeff comes to be 19.5 that means that value of effective nuclear charge is 19.5 * 1.6 * 10^-19 C ? Jul 17, 2020 at 15:46
• @user95732 You are welcome. Strictly speaking, yes, but keep in mind you could be expected to present just $Z_\mathrm{eff}.$ Better clarify with your teacher or whoever gave you the assignment. Jul 17, 2020 at 15:50