The reason for different variation in the size of atoms and the number of electrons.

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Chapter 39, Problem 4Q

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The reason for different variation in the size of atoms and the number of electrons.

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The size of atoms varies by only a factor of three or so,from largest to smallest, yet the number of electrons variesfrom one to over 100. Explain

[#168] Such stuff as dreams are made of. How much of you is not vacuum? Outside of the nucleus, an atom contains mostly empty space. Estimate the fraction of the volume of an atom that is occupied by the nucleus. Assume that a typical atom has a linear dimension of about 0.1 nm and that a typical nuclear dimension is about 1 fm. (Note that this problem introduces some new prefixes: n is nano or 10^{-9}10−9, p is pico or 10^{-12}10−12, f is femto or 10^{-15}10−15). Give your answer as a power of ten. For example, enter: 10^18, or 10^-3 (for 10^{18}1018 or 10^{-3}10−3).

W | File 70 Paste 14+1+13+1+12+|+11·10 ·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1····1·1·20 Home Document1 - Microsoft Word (Product Activation Failed) Insert Page Layout References Review View T Calibri (Body) 14 T Α Α΄ B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbCc AaBl AaBbCcl BIU abe X, X² A ab T 트플 1 Normal No Spaci... Heading 1 Heading 2 Title Subtitle Font Paragraph G Styles ·2·1·1·····1·1·2·1·3·1·4·1·5·1· 6 · 1 · 7 · 1 · 8 · 1 ·9·1·10·1·11·1·12·1·13· |·14·1·15· |· · |·17· 1 · 18 · | I I I I I ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS The motion of two interacting particles (atoms or nuclei) can be described by the following radial Schrödigner equation d l(l 1) −2² [12 a (rªd) – (C,+¹) + V(r)]Re(k;r) = ERe(k;r). 2μ dr where Re(r) is the radial wave function, μ = 2, the reduced mass, V the interacting potential, my+m₂ E the total energy, and k the wave number, given by k = 2μE h² 2. Using Re(k,r) = u₂(k,r) kr show that the above Schrödigner equation reduces to l(l + 1)_24² ď² +…