Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 44, Problem 19SP
To determine
To show: The next nonreactive element after helium is neon
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3. Consider a monatomic linear with equilibrium separation a. Suppose the outer
electrons (of mass m) in a given atom move with a displacement different from that
of the corresponding ion core (of mass M). Let the displacement of the ion core s be:
Us = uei(Ksa-wt)
and the displacement of the center of mass of the outer electrons associated with ion s
be:
V = vei(Ksa-wt)
Each ion core is assumed to interact only with its own outer electrons with a force
proportional to the displacement of the electron distribution from the nucleus, and the
force constant is C₂. However, neighboring electron distributions interact with a force
constant C₁.
a) Show that
-w² Mus = C₂ (vs - Us)
-w²mvs = C₂ (us - Vs) + C₁ (Vs+1 + Vs-1-2vs)
b) Substitute for the displacements, and solve the resulting simultaneous equations.
Find an expression for w².
c) Take the limit as m → 0 (the mass of electrons is much smaller than that of the ion
core), and show that the dispersion relation for the acoustic mode is…
A certain element has its outermost electron in a 3p subshell. It has valence +3 because it has three more electrons than a certain noble gas. What element is it?
In another universe, the electron is a spin@3/2 rather than a spin@1/2 particle, but all other physics are the same as in our universe. In this universe what are the atomic numbers of the lightest two inert gases?
Chapter 44 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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