Effective nuclear charge is the force of attraction of the nucleus on an electron after the repulsive force of the electrons has been broken down. It is found through the formula Z(effective)=ZS, where Z is the positive charge and S is the number of electrons in fully occupied orbitals. The effective nuclear charge of an atom is equal to the number of valence electrons. The simplified equation is sufficient for most purposes, but more complex versions account for the negative charge of valence electrons and deviations in ions.
Effective nuclear charge is the force of attraction of the protons in the nucleus of an atom on an electron after the repulsive force of the atom’s electrons has been broken down. The numerical value of this charge is found through the simple mathematical formula, Z(effective)=ZS, where Z is the positive charge and S is the number of electrons in fully occupied orbitals. In neutral atoms, the effective nuclear charge is equal to the number of electrons in the outermost orbital, which are called valence electrons.
In atoms, protons all have a positive charge of one. An atom is distinguished from other atoms by the number of protons it has, although the number of neutrons can vary between different atoms of the same type and some atoms of the same type can have ions with more or fewer electrons in orbit. The total positive charge of an atom is the number of its protons, which is also the atomic number of the atom as shown in the periodic table of elements. The first step in determining an atom’s effective nuclear charge is to determine its total positive charge, which can be obtained by looking up the atom’s atomic number.
The electrons are attracted towards the nucleus of the atom and are found in orbitals which fill in a predictable way. The first orbital can hold only two electrons. Subsequent orbitals each hold eight electrons when filled. Under normal circumstances, and for the purpose of finding the effective nuclear charge of an atom, the electrons will occupy the orbital closest to the nucleus as possible.
Fully occupied orbitals oppose the same amount of positive charge as they contain negative charge. For example, an atom with 12 protons and 12 electrons, which is a neutral atom, will lose 2 positive charges from the first fully occupied orbital and 8 positive charges from the second. The other two electrons in the third orbital do not affect the atom’s effective nuclear charge, which in this case would be 12 minus 10, or 2.
In most cases, the simplified equation is sufficient to find out the effective nuclear charge of an atom. More complex versions of the equation account for the small negative charge of the valence electrons, which is considered negligible for most purposes. The ions will also have an effective nuclear charge that deviates slightly from the standard equation, as adding an extra electron to the outer orbital will make it slightly less positive, and losing an electron will increase the atom’s positive attraction.
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