PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
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ISBN: 9781319336127
Author: Tipler
Publisher: MAC HIGHER
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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…
. In the Bohr model of the hydrogen atom, an electron in the lowest energy state
follows a circular path.
[ Charge (q) = 1.6 x 10-19 C Coulomb's constant (k) = 8.89 x 10° N.m²/C?. Mass of
electron (me) = 9.109 x 10-31 kg Plank's constant (h) = 6.63 x 10 34 J.s Bohr radius
(ao) = 0.0529 nm]
a) What distance does an electron in the ground state travel?
b) Determine the velocity of the electron around its orbit.
c) What is the effective current associated with this orbiting electron?
%3D
%3D
An electron revolves around the nucleus of an atom
in a circular orbit of radius
4.0Å with a speed of 6.0 x 10^6 ms-1. Calculate the
linear kinetic energy.
Chapter 36 Solutions
PHYSICS F/SCIEN.+ENGRS. W/SAPLING >IC<
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