Recall that the electron probability density is greatest at r = 0 (part (b) in Figure 1.2.1), so the density of dots is greatest for the smallest spherical shells in part (a) in Figure 1.2.1. In effect, we are dividing the atom into very thin concentric shells, much like the layers of an onion (part (a) in Figure 1.2.1), and calculating the probability of finding an electron on each spherical shell. In contrast, we can calculate the radial probability (the probability of finding a 1 s electron at a distance r from the nucleus) by adding together the probabilities of an electron being at all points on a series of x spherical shells of radius r 1, r 2, r 3,…, r x − 1, r x. At very large values of r, the electron probability density is very small but not zero. The probability density is greatest at r = 0 (at the nucleus) and decreases steadily with increasing distance. The 1 s orbital is spherically symmetrical, so the probability of finding a 1 s electron at any given point depends only on its distance from the nucleus. Because Ψ 2 gives the probability of finding an electron in a given volume of space (such as a cubic picometer), a plot of Ψ 2 versus distance from the nucleus ( r) is a plot of the probability density. One way of representing electron probability distributions was illustrated in Figure 6.5.2 for the 1 s orbital of hydrogen. In contrast to his concept of a simple circular orbit with a fixed radius, orbitals are mathematically derived regions of space with different probabilities of having an electron. \)Īn orbital is the quantum mechanical refinement of Bohr’s orbit.
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