Consider Z= 19 potassium. As a rough approximation, assume that each of its n = 1 electrons orbits 19 protons and half an electron—that is, on average, half its fellow n = I electron. Assume that each of its n = 2 electrons orbits 19 protons, two 1s electrons, and half of the seven other n = 2 electrons. Continue the process, assuming that electrons at each J; orbit a correspondingly reduced positive charge. (At each n; an electron also orbits some of the electron clouds of higher a, but we ignore this in our rough approximation.) (a) Calculate in terms of ao the orbit radii of hydrogenlike atoms of these effective Z. (b) The radius of potassium is often quoted at around 0,22 nm. In view of this, are your n = I through n = 3 radii reasonable? (c) About how many more protons would have to be "unscreened" to the n = 4 electron to agree with the quoted radius of potassium? Considering the shape of its orbit, should potassium's n = 4 electron orbit entirely outside all the lower-n electrons?
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