Thanks! One facet of the central field approximation for many-electron atoms is

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Thanks!

One facet of the central field approximation for many-electron atoms is that inner-shell electrons screen the nuclear charge. To understand how this works quantitatively, first note that the probability distributions for electrons in different shells generally do not overlap much. For instance, the electrons in the M shell (n = 3) are almost always farther from the nucleus than the electrons of the K (n = 1) and L (n = 2) shells. Thus, it is a good approximation to assume that the inner shells completely screen the nucleus from the outer shells. For example, if there are ten electrons altogether in the K and L shells of an atom, then the electrons in the M shell experience force from a charge of roughly Z - 10, where Z is the charge on the nucleus as an integer multiple of e, the magnitude of the charge on an electron. This is called the effective nuclear charge Zeff. In a beryllium atom (Z = 4), how many electrons are in the K shell? Express your answer as an integer. In xenon (Z = 54), what is the effective charge Zeff experienced by an electron in the M(n = 3) shell? Express your answer as an integer. How many electrons are there altogether in the K, L, and M shells of xenon? Recall that for n = 3, the orbital quantum number l must be zero, one, or two and that m1 can take any value between positive and negative l. Express your answer as an integer. The idea of simply subtracting the number of inner-shell electrons works well only for atoms with low values of Z. For atoms with larger nuclear charge, the different shapes of the probability distributions for different subshells becomes an important factor. For instance, in the N shell, electrons in the s subshell have a much higher probability than those in the p or d subshells of being found closer to the nucleus than some of the K, L, or M electrons. It is said that the s electrons penetrate the inner shells more readily than do the p or d electrons. Therefore, it is to be expected that our simple subtraction model may not work well for outer-shell s electrons in large atoms. Keeping this in mind, we see that the effective nuclear charge Zeff for the outermost electron in an atom may be found experimentally by measuring the ionization energy of an atom and then calculating the effective charge using the equation En = - /n2(13.6 eV). The energy for the 5p valence electron in indium (Z = 49) is - 5.79 electron volts. What is the effective nuclear charge Zeff experienced by this electron? Express your answer to three significant figures.

Explanation / Answer

a) 2

b) zero

c) 28

d) 3

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