In the Spherical Cluster Approximation, a cluster is modeled as a sphere with the volume of the cluster assumed equal to the number of atoms N in the cluster multiplied with the volume of one atom. Using this model, derive expressions for: (a) the radius of the cluster, Rc in terms of the radius of an atom, Ra. (b) the surface area of the cluster, Sc, in terms of the surface area of an atom, Sa. (c) the number of surface atoms, Ns (assume that this is equal to the surface area of the cluster divided by the cross sectional area of an atom) (d) The fraction of atoms on the surface.
In the Spherical Cluster Approximation, a cluster is modeled as a sphere with the volume of the cluster assumed equal to the number of atoms N in the cluster multiplied with the volume of one atom. Using this model, derive expressions for: (a) the radius of the cluster, Rc in terms of the radius of an atom, Ra. (b) the surface area of the cluster, Sc, in terms of the surface area of an atom, Sa. (c) the number of surface atoms, Ns (assume that this is equal to the surface area of the cluster divided by the cross sectional area of an atom) (d) The fraction of atoms on the surface.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
Provide an answer for Part "d" only.
Transcribed Image Text:In the Spherical Cluster Approximation, a cluster is modeled as a sphere with the volume of the
cluster assumed equal to the number of atoms N in the cluster multiplied with the volume of
one atom. Using this model, derive expressions for:
(a) the radius of the cluster, Rc in terms of the radius of an atom, Ra.
(b) the surface area of the cluster, Sc, in terms of the surface area of an atom, Sa.
(c) the number of surface atoms, Ns (assume that this is equal to the surface area of the
cluster divided by the cross sectional area of an atom)
(d) The fraction of atoms on the surface.
Expert Solution
Step 1
Answer-d
This question is based on extensive properties and as volume is an extensive property therefore it is additive.
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