Hydrogen boundary surface diagrams

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 7.18 (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. 

The solutions of the Schrodinger equation show how / is distributed in the space around the nucleus of the hydrogen atom. The solutions for t are characterized by the values of three quantum numbers (essentially there are three because of the three spatial dimensions, x, y and z), and every allowed set of values for the quantum numbers, together with the associated wave function, describes what is termed an atomic orbital. Other representations are used for atomic orbitals, such as the boundary surface and other diagrams described later in the chapter, but the strict definition of an atomic orbital is its mathematical wave function. 

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