The shapes of p orbitals

Now we turn our attention to the p orbitcds (orbitals with / = 1), which have a double-lobed appearance like that shown in Fig. 9.48. The two lobes are separated by a nodal plane that cuts through the nucleus. There is zero probability density 

Note that because y/ is proportional to r, it is zero at the nucleus, so there is zero probability of finding the electron in a small volume centered on the nucleus. The orbital is also zero everywhere on the plane with cos = 0, corresponding to 8 = 90°. The p, and p orbitals are similar but have nodal planes perpendicular 

The exclusion of the electron from the region of the nucleus is a common feature of all atomic orbitals except s orbitals. To understand its origin, we need to recall from Section 9.5 that the value of the quantum number I tells us the magnitude of the angular momentum of the electron around the nucleus (eqn 9.26, 7 = /(/ -t For an s orbital, the orbital angular momentum is zero (because 

Each p subshell consists of three orbitals (m = -1-1,0, -1). The three orbitals are normally represented by their boundary surfaces, as depicted in Fig. 9.48. The orbital has a symmetrical double-lobed shape directed along the x-axis, and similarly the py and p orbitals are directed along they- and z-axes, respectively. As n increases, the p orbitals become bigger (for the same reason as s orbitals) and have n - 2 radial nodes. However, their boundary surfaces retain the double-lobed shape shown in the illustration. 

An s electron (an electron described by an s orbited) hcis j/=0 cuid has no angular momentum about any axis. A p electron C ui circulate clockwise about an axis as seen from below mi = -i-l). Of its toted euiguleff momentum of 2 h = l.4l4h, an amount h is due to motion effoimd the selected eixis (the rest is due to motion around the other two axes). A p electron can also circulate counterclockwise as seen from below (m/ = -1) or not at all mi = 0) about that selected axis. 

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What happens with the second principal energy level (n = 2) Here we find two sublevels, 2s and 2p. Like Is in the first principal energy level, the 2s orbital is spherical in shape but is larger in size and higher in energy. It also holds a maximum of two electrons. The second type of orbital is designated by 2p. The 2p sublevel consists of three orbitals 2p, 2py, and 2p. The shape of p orbitals is quite different from the s orbitals, as shown in Figure 10.9. 

The orbitals occupied by p, d, and/electrons have three-dimensional shapes different from those of the electrons. There are three p orbitals, starting with n = 2. Each p orbital has two lobes like a balloon tied in the middle. The three p orbitals are arranged in three perpendicular directions, along the x, y, and z axes around the nucleus (see Figure 5.7). As with s orbitals, the shape of p orbitals is the same, but the volume increases at higher energy levels. 

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