Answered: Explain the structure of the atom in…

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Physics

Explain the structure of the atom in general

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter8: Atomic Structure

Section: Chapter Questions

Problem 7CQ: Explain how a hydrogen atom in the ground state (l = 0) can interact magnetically with an external...

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Concept explainers

The Bohr model

Students often get confused between Rutherford’s model and Bohr model of an atom. They interpret the postulates of both these models to be the same, which is incorrect. Rutherford’s model differs from Bohr’s model in the following ways:

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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…
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