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Atkins' Physical Chemistry | 11th Edition | ISBN: 9780198769866 | Authors: Atkins, Peter; De Paula, Julio; Keeler, James ISBN: 9780198769866 2042

Solution for problem P11C.6 Chapter 11C

Atkins' Physical Chemistry | 11th Edition

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Atkins' Physical Chemistry | 11th Edition | ISBN: 9780198769866 | Authors: Atkins, Peter; De Paula, Julio; Keeler, James

Atkins' Physical Chemistry | 11th Edition

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Problem P11C.6

The Morse potential energy (eqn 11C.7) is very useful as a simple representation of the actual molecular potential energy. When \({ }^{85} \mathrm{Rb}^{1} \mathrm{H}\) was studied, it was found that \(\tilde{v}=936.8 \mathrm{~cm}^{-1}\) and \(x_{\mathrm{e}} \tilde{v}=14.15 \mathrm{~cm}^{-1}\). Plot the potential energy curve from 50pm to 800pm around \(R_{e}\) = 236.7pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting \(V^{*}\) = V + hc BJ(J + 1) with \(\tilde{B}=\hbar / 4 \pi c \mu R^{2}\). Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotation. Hints: Taking \(\tilde{B}=3.020 \mathrm{~cm}^{-1}\) as the equilibrium bond length will greatly simplify the calculation. The mass of \({ }^{85} \mathrm{Rb}\) is 84.9118\(m_{u}\).

Text Transcription:

^85Rb^1H

v=936.8cm^-1

xev=14.15cm^-1

R_e

tildeB=h/4picmuR^2

V^*

tildeB=3.020cm^-1

M_u

^85Rb

Step-by-Step Solution:
Step 1 of 3

11/3/19 Chem 121 Ch 7 - Atomic radius bonding: one half of distance between covalently bonded nuclei - Nuclear charge and number of protons impact, the bigger the nuclear charge= the bigger attraction for electrons - Shell number: highest n quantum number - Atomic radius DECREASES from left to right across period, more protons increase in nuclear attraction for valence electrons - Atomic radius INCREASES going down each group, effective nuclear charge is the same - Radius: distance between nucleus and valence electrons ATOMIC RADIUS EXAMPLES - Largest atomic radius; F Ge K Rb Br - Rb is the largest - In order: F K Ge Br Rb - In order: S SE Te - In order: F Si Ba Ionization energy: ability of an element to lose and electron - Ionization potential: energy needed to remove 1st loosely bound electron - Second ionization energy: energy needed to remove the 2nd - Valence electrons are easier to remove than inner core electrons - Ionization energy INCREASES from left to right IONIZATION ENERGY EXAMPLES - Which atom has the smallest IE - Ba Sr Ca 1 11/3/19 - K Ga As Electron affinities increase from left to right but increases irregularly - The more negative = the more electrons its attracting - It becomes more exothermic as you go from left to right - 2

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Chapter 11C, Problem P11C.6 is Solved
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Textbook: Atkins' Physical Chemistry
Edition: 11
Author: Atkins, Peter; De Paula, Julio; Keeler, James
ISBN: 9780198769866

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