How to find Effective Nuclear Charge (ENC)?

Effective Nuclear Charge

According to Wikipedia, In atomic physics, the effective nuclear charge is the actual amount of positive (nuclear) charge experienced by an electron in a multi-electron atom.

The symbol of effective nuclear charge is Zeff or Z*. ENC is the net positive charge experienced by an electron in a multi-electron atom. The effective nuclear charge on an atom is given by equation-

Zeff = Z – S
Where,

• Z = The number of protons in the nucleus (atomic number).
• S = The number of electrons between the nucleus and the electron in question (the number of nonvalence electrons).

Question: Consider a neutral neon atom (Ne), a sodium cation (Na+), and a fluorine anion (F–). What is the effective nuclear charge for each?

Solution:

Start by figuring out the number of nonvalence electrons, which can be determined from the electron configuration.
Ne has 10 electrons. The electron configuration is 1s22s2 2p6. The valence shell is shell 2 and contains 8 valence electrons. Thus the number of nonvalence electrons is 2 (10 total electrons – 8 valence). The atomic number for neon is 10, therefore:

Zeff(Ne) = 10 – 2 = 8+

Flourine has 9 electrons but F– has gained an electron and thus has 10. The electron configuration is the same as for neon and the number of nonvalence electrons is 2. The atomic number for F– is 9, therefore:

Zeff(F–) = 9 – 2 = 7+

Sodium has 11 electrons but the Na+ ion has lost an electron and thus has 10. Once again, the electron configuration is the same as in the previous examples and the number of nonvalence electrons is 2 (by losing one electron, the valence shell becomes the n=2 shell). The atomic number for Na+ is 11, therefore:

Zeff(Na+) = 11 – 2 = 9+

In each of the above examples (Ne, F–, Na+) an atom has 10 electrons but the effective nuclear charge varies because each has a different atomic number. The sodium cation has the largest effective nuclear charge, which results in electrons being held the tightest, and therefore Na+ has the smallest atomic radius.

Practice Questions...

1. Find ENC on Chlorine atom.
2. Consider a neutral argon atom (Ar), a magnesium cation (Mg+), and a fluorine anion (F–). What is the effective nuclear charge for each?

In closing...

In this blog we learnt how to calculate effective nuclear charge on any atom. Using this method you can try differnt atomic configuration to find ENC. If you need more help about chemistry read our blogs HERE.