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**Hint:**The effective nuclear charge is the net positive charge experienced by an electron. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom. Most of the physical and chemical properties of the elements can be explained on the basis of electronic configuration.

**Complete answer:**

The effective nuclear charge is the net positive charge experienced by an electron in a poly electronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons.

We are given that, effective nuclear charge is $2.60$ and contains three valence shell electrons.

Thus, the minimum number of main shells for the given element are two.

So the electronic configuration will be $1{s^2},2{s^2},2{p^1}$

so the total number of electrons is $5$ .

It is the same for the neutral atom.

Therefore, number of electrons$ = $Atomic number

So, the atomic number of the element is $5$.

**Additional information:**

The effective nuclear charge experienced by the electron is also called the core charge. Consider the behavior of ionization energies in the periodic table. It is known that the magnitude of ionization potential depends upon the following factors:

$ - $Size of atom;

$ - $The nuclear charge;

$ - $The screening effect of the inner shells.

$ - $The extent to which the outermost electron penetrates into the charge cloud set up by the inner lying electron

**Note:**

The effective nuclear charge is always less than the total number of protons present in a nucleus due to shielding effect. Effective nuclear charge is behind all other periodic table tendencies. The screening constants contain little chemical insight as a qualitative model of atomic structure.

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