Question

The formula for an effective nuclear charge is:
(if \[\sigma \]is screening constant)
(A) \[Z-\sigma \]
(B) \[Z+\sigma \]
(C) \[Z{{\sigma }^{-1}}\]
(D) \[Z\sigma \]

Answer 1

Hint: The effective nuclear charge (\[{{Z}_{eff}}\]) is nothing but the net positive charge practised by valence electrons. There is a mathematical formula to calculate it. The effective nuclear charge that is practised by an electron in an atom containing more than one electron is usually less for electrons that are shielded by the core electrons.

Complete step by step solution:
-The effective nuclear charge can be expressed in the form of an equation as follows.
\[{{Z}_{eff}}=Z-\sigma \]
where, ‘Z’ is the atomic number and ‘\[\sigma \]’is the screening constant or the number of shielding electrons in the same atom.
-The word ‘effective’ is used due to the shielding effect of the charge of the electrons (negatively charged) inhibits electrons which are present in a higher orbital to go through the full nuclear charge.
-If an electron is present so far from the nucleus means present at a longer distance from the nucleus, then many of the other electrons will be present in between that electron and the nucleus.
-Therefore the electrons present in between the last electron and nucleus will reduce a portion of the positive charge of the nucleus on the outermost electron.
-So, the attraction between the outermost electron and nucleus decreases.
-Consequently, the electron which is present in the outermost shell experiences less effective nuclear charge (\[{{Z}_{eff}}\]) than the original nuclear charge (Z). This is called shielding of electrons.

So, the correct option is (A).

Note: If an atom has very few electrons (like one or two) in its orbitals. Then the effective nuclear charge (\[{{Z}_{eff}}\]) experienced by the electrons is high due to the distance between the electrons and nucleus is less and shielding by other electrons is also less.