Radial probability distribution plot

Figure 7.19 The 2p orbitals. A, A radial probability distribution plot of the 2p orbital shows a single peak. It lies at nearly the same distance from the nucleus as the larger peak in the 2s plot (shown in Figure 7.18B). B, A cross section shows an electron cloud representation of the 90% probability contour of the 2p orbital. An electron occupies both regions of a 2p orbital equally and spends 90% of its time within this volume. Note the nodal plane at the nucleus. C, An accurate representation of the 2pj probability contour. The 2p and 2py orbitals lie along the x and y axes, respectively. D, The stylized depiction of the 2p probability contour used throughout the text. E, In an atom, the three 2p orbitals occupy mutually perpendicular regions of space, contributing to the atom s overall spherical shape.

The electron s wave function (iK atomic orbital) is a mathematical description of the electron s wavelike behavior in an atom. Each wave function is associated with one of the atom s allowed energy states. The probability density of finding the electron at a particular location is represented by An electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus for a particular energy level. Three features of an atomic orbital are described by quantum numbers size (n), shape (/), and orientation (m/). Orbitals with the same n and / values constitute a sublevel sublevels with the same n value constitute an energy level. A sublevel with / = 0 has a spherical (s) orbital a sublevel with / = 1 has three, two-lobed (p) orbitals and a sublevel with / = 2 has five, multi-lobed (d) orbitals. In the special case of the H atom, the energy levels depend on the n value only. 

Distinguish between i / (wave function) and i (probability density) understand the meaning of electron density diagrams and radial probability distribution plots describe the hierarchy of quantum numbers, the hierarchy of levels, sublevels, and orbitals, and the shapes and nodes of s, p, and d orbitals and determine quantum numbers and sublevel designations ( 7.4) (SPs 7.4-7.6) (EPs 7.35-7.47)... 

For each of the s orbitals, a plot of probability density vs. distance (top, with the relief map, inset, showing the plot in three dimensions) lies above a quarter section of an electron cloud depiction of the 90% probability contour (middle), which lies above a radial probability distribution plot (bottom). A,The Is orbital. B,The 2s orbital. C,The 3s orbital. 

Figure 7.18 The 3rf orbitals. A, A radial probability distribution plot. B. Cross section of an electron cloud depiction of the orbital probability contour shows two mutually perpendicular nodal planes and lobes lying between the axes. C. An accurate representation of the orbital probability contour. D,The stylized depiction of the 3dy orbital used in the text. E,The 3d orbital. F.The 3d orbital. G,The lobes of the d 2 2 orbital lie a/ongr the x and y axes. H.The d orbital has two lobes and a central, donut-shaped region. I, A composite of the five 3d (stylized) orbitals shows how they contribute to the atom s spherical shape.

The probability density of finding the electron at a particular location is represented by > (2. For a given energy level, an electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus. 

All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases. The radial probability distribution for the Is orbital exhibits a maximum at 52.9 pm (0.529 A) from the nucleus. Interestingly, this distance is equal to the radius of the n = 1 orbit in the Bohr model of the hydrogen atom. The radial probability distribution plots for the 2s and 3s orbitals exhibit two and three maxima, respectively, with the greatest probability occurring at a greater distance from the nucleus as n increases. Between the two maxima for the 2s orbital there is a point on the plot where the probability drops to zero. This corresponds to a node in the electron density, where the standing wave has zero amplitude. There are two such nodes in the radial probability distribution plot of the 3s orbital. 

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