Quantum shells, principal

The explanation of these facts is not difficult but is subtle. We recall that the energies of all hydrogen orbitals belonging to the same principal quantum shell (n) are equal the >d, 3p and 35 hydrogen orbitals are degenerate. These orbital subsets... 

For given n and / = 0 there is only one possible orbital, namely, one with m = 0. Thus there is only one s orbital of each principal quantum shell. For given n and / = 1 there are three possible m values. Hence each principal shell has three different p orbitals. Similarly, d orbitals come in sets of five, / orbitals in sets of seven, and so on. In the absence of any external forces, the energy of an orbital is independent of its m value. Hence all three np orbitals, all five nd orbitals, and so on, are of the same energy. 

The atomic radii of the second- and third-series transition elements from group 4B on are nearly identical, though we would expect an increase in size on adding an entire principal quantum shell of electrons. The small sizes of the third-series atoms are associated with what is called the lanthanide contraction, the general decrease in atomic radii of the /-block lanthanide elements between the second and third transition series (Figure 20.4). 

Octet expansion or hypervalent state is due to the involvement of d-orbitals of the same principal quantum shell (e.g., 3d in third period, 4d in fourth period, etc.). The two other factors that play a role in octet expansion are ... 

The pairing of electrons is important, because it confers a degree of stability on the species concerned. Electrons in an atom are contained within atomic orbitals, each of which may only hold a maximum of two electrons. The electron in a hydrogen atom is contained in the first principal quantum shell, which is indicated by 1. Within this principal quantum shell, there is only one type of subshell, and this is represented by the letter s . The electronic configuration of hydrogen may be written as Is1. The raised postscript indicates that there is only one electron in that particular orbital. 

The two electrons in helium are both contained within the first principal quantum shell. Write down the electronic configuration of helium. 

In the second principal quantum shell, there are four subshells, one s and three p subshells, each of which may contain two electrons, which gives a total of eight electrons in all at the second level. 

The electron that was added to the helium atom to form the anion could not fit into the s subshell of the first principal quantum shell, because it already had two electrons and so was full. Instead, this extra electron occupied the next available orbital, which was the s subshell of the second principal quantum level. This requires a lot of energy, and so it is difficult. Hence, the He- anion, which it should also be noted is a radical species, is not normally found. 

As each element in the second row has four subshells in the second principal quantum level, and as each subshell may only accommodate a maximum of two electrons, the result is that no element in the second row may have more than eight electrons in the second principal quantum shell. This is called the Octet rule, and is one of the most fundamental rules concerning the electron distribution around second row elements. Under normal conditions, it is never violated. 

The third row elements have more subshells in their valance shell, i.e. the third principal quantum shell, than the second row elements, namely one s subshell, three p subshells and five d subshells. This means that they may accommodate a maximum of 18 electrons. As far as the organic chemist is concerned, the important consequence of this is that the elements phosphorus and sulphur may expand their octet and have five or six bonds respectively, instead of being limited to just four bonds as is the case with carbon and other second row elements. 

Electrons in an atom are contained within atomic orbitals, each of which may only hold a maximum of two electrons. The principal quantum shell is indicated by a number, e g. 1, 2, 3, etc. Within each shell, there may exist a number of subshells s, p, d and f, depending upon which shell is being considered. There is only one s subshell, while there are three p subshells, which are degenerate pr, pv and pz Hund s rule states that if electrons are placed in degenerate orbitals, they... 

Valence electrons (6.5) The electrons in an atom s highest occupied principal quantum shell, plus any electrons in partially filled subshells of lower principal quantum number. The electrons available for bond formation. 

Assume that the helium wavefunction is a product of two hydrogen-like wavefunctions (that is, neglect the term for the repulsion between the electrons) in the n = 1 principal quantum shell. Determine the electronic energy of the helium atom and compare it to the experimentally determined energy of —1.265 X 10 J. (Total energies are determined experimentally by measuring how much energy it takes to remove all of the electrons from an atom.)... 

Example 12.3 for the helium atom assumed that both electrons have a principal quantum number of 1. If the hydrogen-like wavefunction analogy were taken further, we might say that both electrons are in the s subshell of the first shell—that they are in Is orbitals. Indeed, there is experimental evidence (mostly spectra) for this assumption. What about the next element, Li It has a third electron. Would this third electron also go into an approximate Is hydrogen-like orbital Experimental evidence (spectra) shows that it doesn t. Instead, it occupies what is approximately the s subshell of the second principal quantum shell It is considered a 2s electron. Why doesn t it occupy the Is shell ... 

However, this is misleading. Although electronic energy levels are dictated by the principal quantum number, we should remember that a principal quantum shell in a hydrogen atom has other quantum numbers, namely, f and m. If the symmetries of the operator and wavefunctions in equation 15.1 were examined, one would find that it is the angular momentum quantum number that dictates the selection rule. The specific selection rule for allowed electronic transitions in the hydrogen atom (or, for that matter, hydrogen-like atoms) is... 

Table 3.1 shows the number of electrons in each of the principal quantum shells (energy levels) for the first 11... 

Write the simple electronic configuration of the following atoms, showing the principal quantum shells only ... 

For example, for the 5th ionisation energy of nitrogen, the electron being removed is from the 2nd principal quantum shell. For the 6th ionisation energy of nitrogen, the electron being removed is from the 1st principal quantum shell. 

The principal quantum shells, apart from the first, are split into subshells (sublevels). Each principal quantum shell contains a different number of subshells. The subshells are distinguished by the letters s, p or d. There are also f subshells for elements with more than 57 electrons. Figure 3.6 shows the subshells for the first four principal quantum... 

Figure 3.6 The subshells for the first four principal quantum shells.

An s orbital has a spherical shape. The 2s orbital in the second principal quantum shell has the same shape as the Is orbital in the first quantum shell. They are both spherical, but electrons in the 2s orbital have more energy than electrons in the Is orbital. There are three 2p orbitals in the second quantum shell. Each of these has the same shape. The shape is like an hourglass with two lobes . The three sets of lobes are arranged at right angles to each other along the x, y and z axes. Hence the three 2p orbitals are named 2p, 2p and 2p. The three 2p orbitals have the same energy as each other. There are also three 3p orbitals in the third quantum shell. Their shapes are similar to the shapes of the 2p orbitals. 

The positively charged ions have effectively lost their outer shell of electrons (the third principal quantum shell or energy level) from their original atoms. Hence the cations are much smaller than their atoms. To add to this effect, there is also less shielding of the outer electrons in these cations compared with their original atoms. 

The negatively charged ions are larger than their original atoms. This is because each atom will have gained one or more extra elections into their third principal quantum shell, increasing the repulsion between its electrons, whereas the nuclear charge remains constant. This increases the size of any anion compared with its atom. 

Periods in the Periodic Table are rows of elements whose outermost electrons are in the same principal quantum shell. 

The elements in Group 2 of the Periodic Table are sometimes referred to as the alkaline earth metals. As they are in Group 2, the elements have atoms whose electronic configurations end with two electrons in their outermost principal quantum shell. These two outer electrons occupy an s subshell. Here are the electronic configurations of the first five elements in Group 2 ... 

Took at the metallic radii of the Group 2 elements, shown in Table 11.1. The atoms of Group 2 elements get larger going down the group as the outer two electrons occupy a new principal quantum shell further from the nucleus. 

In this chapter we will look at the elements in Group 17 of the Periodic Table, called the halogens. Their atoms all have seven electrons in the outer principal quantum shell. Here are the electronic configurations of the first four elements in Group 17 ... 

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