Quantum Physics

916 Chapter 28 Atomic PhysicsTIP 28.2 The Electron Isn’tReally SpinningThe electron is not physicallyspinning. Electron spin is a purelyquantum effect that gives theelectron an angular momentum as ifit were physically spinning.Any classical description of electron spin is incorrect because quantum mechanicstells us that since the electron can’t be located precisely in space, it cannot beconsidered to be a spinning solid object, as pictured in Figure 28.11. In spite ofthis conceptual difficulty, all experimental evidence supports the fact that an electrondoes have some intrinsic property that can be described by the spin magneticquantum number.The spin quantum number didn’t come from the original formulation of quantummechanics by Schrodinger (and independently, by Heisenberg). The Englishmathematical physicist P. A. M. Dirac developed a relativistic quantum theory inwhich spin appears naturally.EXAMPLE 28.4 The Quantum Numbers for the 2p SubshellGoal List the distinct quantum states of a subshell by their quantum numbers, including spin.ProblemList the unique sets of quantum numbers for electrons in the 2p subshell.Strategy This is again a matter following the quantum rules for n, , and m , and now m s as well. The 2p subshellhas n 2 (that’s the “2” in 2p) and 1 (that’s from the p in 2p).SolutionBecause 1, the magnetic quantum number can havethe values 1, 0, 1, and the spin quantum number is always 1 2 or 1 2. Consequently, there are 3 2 6 possiblesets of quantum numbers with n 2 and 1,listed in the table at right.n m m s2 1 12 1 12 1 02 1 02 1 12 1 1 1 212 1 212 1 212Remark Remember that these quantum states are not just abstractions; they have real physical consequences, suchas which electronic transitions can be made within an atom and, consequently, which wavelengths of radiation can beobserved.Exercise 28.4(a) How many different sets of quantum numbers are there in the 3d subshell? (b) How many sets of quantum numbersare there in a 2d subshell?Answers (a) 10 (b) None. A 2d subshell doesn’t exist because that would imply a quantum state with n 2 and 2, impossible because n 1.28.8 ELECTRON CLOUDSThe solution of the wave equation, discussed in Section 27.7, yields a wave function that depends on the quantum numbers n, , and m . We assume that wehave found such a wave function and see what it may tell us about the hydrogenatom. Let n 1 for the principal quantum number, which corresponds to the lowestenergy state for hydrogen. For n 1, the restrictions placed on the remainingquantum numbers are that 0 and m 0.The quantity 2 has great physical significance. If p is a point and V p a verysmall volume containing that point, then 2 V p is approximately the probability offinding the electron inside the volume V p . Figure 28.12 gives the probability perunit length of finding the electron at various distances from the nucleus in the 1sstate of hydrogen. Some useful and surprising information can be extracted from