## Calcium Number Of Valence Electrons

### Valence Electrons

The number of electrons in an electrically-neutral atom is the same as the number of protons in the nucleus. Therefore, the number of electrons in neutral atom of Calcium is 20. Each electron is influenced by the electric fields produced by the positive nuclear charge and the other (Z – 1) negative electrons in the atom.

Calcium has 2 valence electrons. Calcium has 20 electrons so they are arranged 2. Using orbital notation the electron structure is: #1s^(2)2s^(2)2p^(6)3s^(2)3p^(6)4s^(2)# You can see that there are 2 electrons in the outer energy level and these are the valence electrons. The total number of electrons present in the valence shell of an atom are called valence electrons, and there are a total of two electrons present in the valence shell of calcium (4s²). Thus, calcium has two valence electrons.

As was mentioned in a previous section of this chapter, electrons are highly important, because a specific subset of electrons, called valence electrons, are solely-responsible for determining how elements bond with one another. The number of valence electrons that are present in an atom can be determined from that atom's electron configuration. Valence electrons are found in the orbitals associated with an atom's highest occupied energy level. The remaining electrons, which are called inner shell electrons, do not participate in bonding and are, therefore, not important to study.

Consider sulfur's electron configuration, which was determined in the previous section and is replicated below.

1s22s22p63s23p4

Recall that the energy levels in an electron configuration are the leading red numbers that denote the start of a new energy level/orbital combination. Sulfur has electrons in the first, second, and third energy levels, as indicated by the leading red1, 2's, and 3's, respectively. Valence electrons are those found in the highest occupiedenergy level. Therefore, in this case, only those electrons associated with an energy level/orbital combination beginning with a 3 need to be considered. Since two energy level/orbital combinations begin with a 3, both orbitals are selected for further consideration:

3s23p4

The superscripts associated with these orbitals total to 6. Therefore, sulfur has 6 valence electrons.

Example (PageIndex{1})

Determine how many of nitrogen's electrons are classified as valence electrons. Nitrogen's electron configuration, which was determined in the previous section, is shown below.

1s22s22p3

Solution

Nitrogen has electrons in the first and second energy levels, as indicated by the leading red1 and 2's, respectively. Valence electrons are those found in the highest occupiedenergy level. Therefore, in this case, only those electrons associated with an energy level/orbital combination beginning with a 2 need to be considered. Since two energy level/orbital combinations begin with a 2, both orbitals are selected for further consideration:

2s22p3

The superscripts associated with these orbitals total to 5. Therefore, nitrogen has 5 valence electrons.

Exercise (PageIndex{1})

Determine how many of the electrons in each of the following elements are classified as valence electrons. Each element's electron configuration, which was determined in the previous section, is shown below.

1. Neon

1s22s22p6

1. Calcium

1s22s22p63s23p64s2

Answer a
Neon has electrons in the first and second energy levels, as indicated by the leading red1 and 2's, respectively. Valence electrons are those found in the highest occupiedenergy level. Therefore, in this case, only those electrons associated with an energy level/orbital combination beginning with a 2 need to be considered. Since two energy level/orbital combinations begin with a 2, both orbitals are selected for further consideration:

2s22p6

The superscripts associated with these orbitals total to 8. Therefore, neon has 8 valence electrons.
Answer b
Calcium has electrons in the first, second, third, and fourth energy levels, as indicated by the leading red1, 2's, 3's, and 4, respectively. Valence electrons are those found in the highest occupiedenergy level. Therefore, in this case, only those electrons associated with an energy level/orbital combination beginning with a 4 need to be considered. Since only one energy level/orbital combination begins with a 4, only one orbital is selected for further consideration:

4s2

The superscript associated with this orbital is a 2. Therefore, calcium has 2 valence electrons.

### Potassium Number Of Valence Electrons

While an electron configuration represents all of the electrons present in an atom of an element, chemists are only truly interested in an atom's valence electrons, since, as indicated above, those are the electrons that are solely-responsible for determining how elements bond with one another. Therefore, finding a 'shortcut' for determining how many valence electrons are present in an atom would be highly convenient. Such a 'shortcut' does, indeed, exist. In a previous section of this chapter, three systems for labeling the groups, or columns, on the periodic table were presented. The second system, which is called the 'A/B System,' was indicated to provide insight into the electronic character of elements found within that group.

### Number Of Valence Electrons In A Calcium Atom

Again, consider sulfur, S, which, based on its electron configuration, has 6 valence electrons.

Sulfur is located in the 16th column of the periodic table. However, the 'A/B System' is used to label the main group elements. Group 16 is the 6th column in the main group, or 'A-Block,' columns of the periodic table and so is labeled as Group 6A. Note that sulfur's valence electron count matches its group number in the 'A/B System.' This connection applies to nearly all elements found in the main group columns of the periodic table. Helium is the only exception to this rule, as it is found in Group 8A, but only contains two total electrons. This inconsistency invalidates the 'A/B shortcut' method, and the electron configuration method must be employed to determine that both of helium's electrons are valence electrons.

Since the 'A/B System' group number corresponds to the number of valence electrons that are present in an atom, all elements found within the same column have the same number of valence electrons. Since an atom's valence electrons are solely-responsible for determining how elements bond with one another, this commonality in electronic character explains why all of the elements within the same group share similar properties.

Example (PageIndex{2}) Based on its location on the periodic table, determine how many of nitrogen's electrons are classified as valence electrons.

Solution

The 'A/B System' group number indicates the number of valence electrons that are present in an atom. Nitrogen (N) is located in the 15th column of the periodic table. However, the 'A/B System' is used to label the main group elements. Group 15 is the 5th column in the main group, or 'A-Block,' columns of the periodic table and so is labeled as Group 5A. Therefore, nitrogen has 5 valence electrons. (This answer is consistent with the solution to Example (PageIndex{1}).)

Exercise (PageIndex{2})

Based on the periodic table, determine how many of the electrons in each of the following elements are classified as valence electrons.

1. Neon
2. Calcium
Answer a
The 'A/B System' group number indicates the number of valence electrons that are present in an atom. Neon (Ne) is located in Group 18, which is labeled as Group 8A, using the 'A/B System.' Therefore, neon has 8 valence electrons. (This answer is consistent with the solution to Exercise (PageIndex{1}text{a}).)
Answer b
Calcium (Ca) is located in Group 2, which is labeled as Group 2A in the 'A/B System.' Therefore, calcium has 2 valence electrons. (Again, this answer is consistent with the solution to Exercise (PageIndex{1}text{b}).)

Learning Objectives

• To understand the basics of electron shielding and penetration

For an atom or an ion with only a single electron, we can calculate the potential energy by considering only the electrostatic attraction between the positively charged nucleus and the negatively charged electron. When more than one electron is present, however, the total energy of the atom or the ion depends not only on attractive electron-nucleus interactions but also on repulsive electron-electron interactions. When there are two electrons, the repulsive interactions depend on the positions of both electrons at a given instant, but because we cannot specify the exact positions of the electrons, it is impossible to exactly calculate the repulsive interactions. Consequently, we must use approximate methods to deal with the effect of electron-electron repulsions on orbital energies. These effects are the underlying basis for the periodic trends in elemental properties that we will explore in this chapter.

## Electron Shielding and Effective Nuclear Charge

If an electron is far from the nucleus (i.e., if the distance (r) between the nucleus and the electron is large), then at any given moment, many of the other electrons will be between that electron and the nucleus (Figure (PageIndex{1})). Hence the electrons will cancel a portion of the positive charge of the nucleus and thereby decrease the attractive interaction between it and the electron farther away. As a result, the electron farther away experiences an effective nuclear charge ((Z_{eff})) that is less than the actual nuclear charge (Z). This effect is called electron shielding.

As the distance between an electron and the nucleus approaches infinity, (Z_{eff}) approaches a value of 1 because all the other ((Z − 1)) electrons in the neutral atom are, on the average, between it and the nucleus. If, on the other hand, an electron is very close to the nucleus, then at any given moment most of the other electrons are farther from the nucleus and do not shield the nuclear charge. At (r ≈ 0), the positive charge experienced by an electron is approximately the full nuclear charge, or (Z_{eff} ≈ Z). At intermediate values of (r), the effective nuclear charge is somewhere between 1 and (Z):

[1 ≤ Z_{eff} ≤ Z.]

Notice that (Z_{eff} = Z) only for hydrogen and only for helium are (Z_{eff}) and (Z) comparable in magnitude (Figure (PageIndex{2})).

Shielding

Shielding refers to the core electrons repelling the outer electrons, which lowers the effective charge of the nucleus on the outer electrons. Hence, the nucleus has 'less grip' on the outer electrons insofar as it is shielded from them.

(Z_{eff}) can be calculated by subtracting the magnitude of shielding from the total nuclear charge and the effective nuclear charge of an atom is given by the equation:

[ Z_{eff}=Z-S label{4}]

where (Z) is the atomic number (number of protons in nucleus) and (S) is the shielding constant. The value of (Z_{eff}) will provide information on how much of a charge an electron actually experiences.

We can see from Equation ref{4} that the effective nuclear charge of an atom increases as the number of protons in an atom increases (Figure (PageIndex{2})). Therefore as we go from left to right on the periodic table the effective nuclear charge of an atom increases in strength and holds the outer electrons closer and tighter to the nucleus. As we will discuss later on in the chapter, this phenomenon can explain the decrease in atomic radii we see as we go across the periodic table as electrons are held closer to the nucleus due to increase in number of protons and increase in effective nuclear charge.

The shielding constant can be estimated by totaling the screening by all electrons ((n)) except the one in question.

[ S = sum_{i}^{n-1} S_i label{2.6.0}]

where (S_i) is the shielding of the ith electron.

Electrons that are shielded from the full charge of the nucleus experience an effective nuclear charge ((Z_{eff})) of the nucleus, which is some degree less than the full nuclear charge an electron would feel in a hydrogen atom or hydrogenlike ion.

From Equations ref{4} and ref{2.6.0}, (Z_{eff}) for a specific electron can be estimated is the shielding constants for that electron of all other electrons in species is known. A simple approximation is that all other electrons shield equally and fully:

[S_i=1 label{simple}]

This crude approximation is demonstrated in Example (PageIndex{1}).

Example (PageIndex{1}): Fluorine, Neon, and Sodium

What is the effective attraction (Z_{eff}) experienced by the valence electrons in the three isoelectronic species: the fluorine anion, the neutral neon atom, and sodium cation?

Solution

Each species has 10 electrons, and the number of nonvalence electrons is 2 (10 total electrons - 8 valence), but the effective nuclear charge varies because each has a different atomic number (A). This is an application of Equations ref{4} and ref{2.6.0}. We use the simple assumption that all electrons shield equally and fully the valence electrons (Equation ref{simple}).

The charge (Z) of the nucleus of a fluorine atom is 9, but the valence electrons are screened appreciably by the core electrons (four electrons from the 1s and 2s orbitals) and partially by the 7 electrons in the 2p orbitals.

• (Z_mathrm{eff}(mathrm{F}^-) = 9 - 2 = 7+)
• (Z_mathrm{eff}(mathrm{Ne}) = 10 - 2 = 8+)
• (Z_mathrm{eff}(mathrm{Na}^+) = 11 - 2 = 9+)

So the sodium cation has the greatest effective nuclear charge. This also suggests that (mathrm{Na}^+) has the smallest radius of these species and that is correct.

Exercise (PageIndex{1}): Sodium Species

What is the effective attraction (Z_{eff}) experienced by the valence electrons in the sodium anion, the neutral sodium atom, and sodium cation? Use the simple approximation for shielding constants. Compare your result for the sodium atom to the more accurate value in Table (PageIndex{1}) and proposed an origin for the difference.

Answer
• (Z_mathrm{eff}(mathrm{Na}^-) = 11 - 2 = 7+)
• (Z_mathrm{eff}(mathrm{Na}) = 11 - 2 = 8+)
• (Z_mathrm{eff}(mathrm{Na}^+) = 11 - 2 = 9+)

The (Z_{eff}) in Table (PageIndex{1}) for (Z_mathrm{eff}(mathrm{Na}) is 10.63 and appreciables larger than the 8 estimated above. This means the simple approximation (Equation ref{simple}) overestimates the shielding constant (S).

## Electron Penetration

The approximation in Equation ref{simple} is a good first order description of electron shielding, but the actual (Z_{eff}) experienced by an electron in a given orbital depends not only on the spatial distribution of the electron in that orbital but also on the distribution of all the other electrons present. Educated a memoir book review. This leads to large differences in (Z_{eff}) for different elements, as shown in Figure (PageIndex{2}) for the elements of the first three rows of the periodic table.

Penetration describes the proximity to which an electron can approach to the nucleus. In a multi-electron system, electron penetration is defined by an electron's relative electron density (probability density) near the nucleus of an atom (Figure (PageIndex{3})). Electrons in different orbitals have different electron densities around the nucleus. In other words, penetration depends on the shell ((n)) and subshell ((l)).

For example, a 1s electron (Figure (PageIndex{3}); purple curve) has greater electron density near the nucleus than a 2p electron (Figure (PageIndex{3}); red curve) and has a greater penetration. This related to the shielding constants since the 1s electrons are closer to the nucleus than a 2p electron, hence the 1s screens a 2p electron almost perfectly ((S=1). However, the 2s electron has a lower shielding constant ((S<1) because it can penetrate close to the nucleus in the small area of electron density within the first spherical node (Figure (PageIndex{3}); green curve). In this way the 2s electron can 'avoid' some of the shielding effect of the inner 1s electron.

For the same shell value ((n)) the penetrating power of an electron follows this trend in subshells (Figure (PageIndex{3})):

[s > p > d approx f. label{better1}]

for different values of shell (n) and subshell (l), penetrating power of an electron follows this trend:

[ce{1s > 2s > 2p > 3s > 3p > 4s > 3d > 4p > 5s > 4d > 5p > 6s > 4f ..} label{better2}]

Penetration

Penetration describes the proximity of electrons in an orbital to the nucleus. Electrons that have greater penetration can get closer to the nucleus and effectively block out the charge from electrons that have less proximity.

Table (PageIndex{1}): Effective Nuclear Charges for Selected Atoms
AtomSublevelZZeff
H1s11
He1s21.69
Li1s, 2s32.69, 1.28
Be1s, 2s43.68, 1.91
B1s, 2s, 2p54.68, 2.58, 2.42
F1s, 2s, 2p98.65, 5.13, 5.10
Na1s, 2s, 2p, 3s1110.63, 6.57, 6.80, 2.51

Data from E. Clementi and D. L. Raimondi; The Journal of Chemical Physics 38, 2686 (1963).

Because of the effects of shielding and the different radial distributions of orbitals with the same value of n but different values of l, the different subshells are not degenerate in a multielectron atom. For a given value of n, the ns orbital is always lower in energy than the np orbitals, which are lower in energy than the nd orbitals, and so forth. As a result, some subshells with higher principal quantum numbers are actually lower in energy than subshells with a lower value of n; for example, the 4s orbital is lower in energy than the 3d orbitals for most atoms.

A Better Estimation of Shielding: Slater Rules

The concepts of electron shielding, orbital penetration and effective nuclear charge were introduced above, but we did so in a qualitative manner (e.g., Equations ref{better1} and ref{better2}). A more accurate model for estimating electron shielding and corresponding effective nuclear charge experienced is Slater's Rules. However, the application of these rules is outside the scope of this text.

## Summary

The calculation of orbital energies in atoms or ions with more than one electron (multielectron atoms or ions) is complicated by repulsive interactions between the electrons. The concept of electron shielding, in which intervening electrons act to reduce the positive nuclear charge experienced by an electron, allows the use of hydrogen-like orbitals and an effective nuclear charge ((Z_{eff})) to describe electron distributions in more complex atoms or ions. The degree to which orbitals with different values of l and the same value of n overlap or penetrate filled inner shells results in slightly different energies for different subshells in the same principal shell in most atoms.