Size of orbitals

For a given atom, a series of orbitals with different values of n but the same values of / and m/ (e.g. I5, 2s, 3s, 4s.) differ in 

it is assumed that R,., em re normalized. The probability of finding 

For large r, D(r) behaves as r exp(-2Zr/n). This function has the following maximum  

The least bound electrons engage in chemical bonds with other atoms and are therefore called valence electrons. The inner orbitals are called core orbitals. 

For a given atom, a series of orbitals with different values of n but the same values of / and w/ (e.g. Is, 2s, 3s, 4s.) differ in their relative size (spatial extent). The larger the value of n, the larger the orbital, although this relationship is not linear. The relative spatial extents of the Is, 2s and 3s orbitals, and of the 2p and 3p orbitals, are shown in Fig. 1.11. An increase in size also corresponds to an orbital being more diffuse. 

The spin quantum number and the magnetic spin quantum number 

Whereas an atomic orbital is defined by a unique set of three quantum numbers, an electron in an atomic orbital is defined by a unique set of four quantum numbers n, I, mi 

4 Angular momentum, the inner quantum number, /, and spin-orbit coupling 

The value of I determines not only the shape of an orbital but also the amotmt of orbital angular momentum associated with an electron in the orbital  

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Anomeric interactions are also affected by the sizes of the interacting orbitals and will be best where the Y has orbitals of similar size to N. Thns, in an ONCl system, the similarity in size of orbitals on N and O and lower energy of the N—Cl a orbital favours the no-anomeric effect over the alternative nci-[Pg.844]

Which quantum numbers reveal information about the shape, energy, oneniation, and size of orbitals ... 

The sizes of orbitals increase with increasing n and the true shapes of p orbitals are diffuse, as shown in Figure 5-26. The directions of p, d, and / orbitals, however, are easier to visualize in drawings such as those in Figures 5-23, 5-24, and 5-25 therefore, these slender representations are usually used. 

Figure 6.70 The vinylogous anomeric effect, (a) Experimental evidence, (b) Cartoon of overlap of v /2 for an enol ether with the C3-X a. Different sizes of orbitals give an indication of coefficients. A valence bond representation of the effect is also shown.

Patterns of Atomic Structure The Size of Orbitals MiniLab 7.2 Electrons in Atoms... 

The corresponding values of p are represented by vertical lines in Figure 21-3. From this expression it is seen that the size of the atom increases about as the square of the principal quantum number , fnjm being in fact proportional to n2 for the states with 1=0 and showing only small deviations from this proportionality for other states. This variation of size of orbit with quantum number is similar to that of the old quantum theory, the time-average electron-nucleus distance for a Bohr orbit being... 

In defining the sizes of orbitals, why must we use an arbitrary value, such as 90% of the probability of finding an electron in that region ... 

Each bound orbit can be classified in terms of the dimensions (largest and smallest distance to the Sun), with an associated total energy. In classical mechanics, there are no constraints on the energy, and all sizes of orbits are allowed. If the zero point for... 

Orbital energies in a hydrogen-like species Size of orbitals... 

Main energy levels corresponding to electron shells discussed earlier in this chapter are designated by a principal quantum number n. Both the size of orbitals... 

The sizes of orbitals increase with increasing n, as shown in Figure 4-28. How do we know the sizes of orbitals and the relationship between the value of n and orbital size Experiments such as density measurements provide information about atomic radii, and thus about the sizes of the outermost orbitals. In addition, calculations and models of the orbitals enable us to make correct predictions. Figure 4-28 shows an example of the relationship between n and the size of the orbitals. We will find the following generalizations about orbital sizes useful ... 

As has a higher ionization energy than Sb because as you trace the path between As and Sb on the periodic table, you move down a column. Ionization energy decreases as you go down a column as a result of the increasing size of orbitals with increasing n. 

Same size of orbital Same energy of orbital Directionality in space... 

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