Boundary surface diagrams

Figure 6 Boundary surface diagrams for jt/tt molecular orbitals...

FIGURE 7.17 (aj Plot of electron density in the hydrogen 1 s orbital as a function of the distance from the nucleus. The electron density falls off rapidly as the distance from the nucleus increases. (b) Boundary surface diagram of the hydrogen 1 s orbital. 

Figure 7.18 shows boundary surface diagrams for the li, 2s, and 3s hydrogen atomic orbitals. All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases. Although the details of electron density variation within each boundary surface are lost, there is no serious disadvantage. For us the most important features of atomic orbitals are their shapes and relative sizes, which are adequately represented by boundary surface diagrams. 

FIGURE 7.19 The boundary surface diagrams of the three 2p orbitals. These orbitals are identical in shape and energy, but their orientations are different. 

FIGURE 7.20 Boundary surface diagrams of the five 3d orbitals. Although the 3d 2 orbital looks different, it is equivalent to the other four orbitals in all other respects. The d orbitals of higher principal quantum numbers have similar shapes. 

The boundary surface diagrams of p orbitals in Figure 7.19 show that each p orbital can be thought of as two lobes on opposite sides of the nucleus. Like s orbitals, p orbitals increase in size from 2p to 3p to 4p orbital and so on. 

An atomic orbital is a function ip) that defines the distribution of electron density (ip ) in space. Orbitals are represented by electron density diagrams or boundary surface diagrams. 

Actinide series, p. 276 Amplitude, p. 244 Atomic orbital, p. 261 Aufbau principle, p. 274 Boundary surface diagram, p. 264... 

Why is a boundary surface diagram useful in representing an atomic orbital ... 

Figures Boundary surface diagrams for p p and s-r moiecuiar orbitais...

FIGURE 3.8 Atomic orbitals. Boundary surface diagrams for electron densities of Is, 2s. 2p, 3s. 3p, and 3d orbitals. For the p orbitals, the subscript letter on the orbital notation (x, y, z) indicates the cartesian axis along which the orbital lies. 

Figure 7.18 (a) Plot of electron density in the hydrogen 1s orbital as a function of the distance from the nucleus. The electron density falls off rapidly as the distance from the nucleus increases, p) Boundary surface diagram of the hydrogen 1s orbital, p) A more realistic way of viewing electron density distribution is to divide the Is orbital into successive spherical thin shells. A plot of the probability of finding the electron in each shell, called radial probability, as a function of distance shows a maximum at 52.9 pm from the nucleus. Interestingly, this is equal to the radius of the innermost orbit in the Bohr model. 

Figure 7.19 Boundary surface diagrams of the hydrogen 1s, 2s, and 3s orbitals. Each sphere contains about 90 percent of the total electron density. All s orbitals are spherical. Roughly speaking, the size of an orbital is proportional to n, where n is the principal quantum number.

The quantum state of an electron in a hydrogen atom is given by its wavefunction (or atomic orbital) [ip(r, 0, < )] and the distribution of electron density in space is given by tlfir, 0, tf>). The sizes and shapes of atomic orbitals can be represented by electron density diagrams or boundary surface diagrams. 

Although the details of electron density variation within each boundary surface are lost, the most important features of atomic orbitals are their overall shapes and relative sizes, which are adequately represented by boundary surface diagrams. 

The representations are also referred to as boundary-surface diagrams. 

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