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P7E.1 If the vibration of a diatomic A-B is modelled using a harmonic oscillator, the vibrational frequency is given by w=(k; /u)", where u is the effective mass, µ=m,m,/(m, +m,). If atom A is substituted by an isotope (for example H substituted for 'H), then to a good approximation the force constant remains the same. Why? (Hint: Is there any change in the number of charged species?) (a) Show that when an isotopic substitution is made for atom A, such that its mass changes from m, to m, the vibrational frequency of A'-B, wAp can be expressed in terms of the vibrational frequency of A-B, @ An as o x=0 A (H/H", where u AB and u, are the effective masses of A-B and A'-B, respectively. (b) The vibrational frequency of 'HCl is 5.63 x 10"s". Calculate the vibrational frequency of (i) 'H*Cl and (ii) 'H"Cl. Use integer relative atomic masses. A'B

P7E.1 If the vibration of a diatomic A-B is modelled using a harmonic oscillator, the vibrational frequency is given by w=(k; /u)", where u is the effective mass, µ=m,m,/(m, +m,). If atom A is substituted by an isotope (for example H substituted for 'H), then to a good approximation the force constant remains the same. Why? (Hint: Is there any change in the number of charged species?) (a) Show that when an isotopic substitution is made for atom A, such that its mass changes from m, to m, the vibrational frequency of A'-B, wAp can be expressed in terms of the vibrational frequency of A-B, @ An as o x=0 A (H/H", where u AB and u, are the effective masses of A-B and A'-B, respectively. (b) The vibrational frequency of 'HCl is 5.63 x 10"s". Calculate the vibrational frequency of (i) 'H*Cl and (ii) 'H"Cl. Use integer relative atomic masses. A'B

Chemistry
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
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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P7E.1 If the vibration of a diatomic A-B is modelled using a harmonic oscillator, the vibrational frequency is given by w=(k; /u)", where u is the effective mass, µ=m,m,/(m, +m,). If atom A is substituted by an isotope (for example H substituted for 'H), then to a good approximation the force constant remains the same. Why? (Hint: Is there any change in the number of charged species?) (a) Show that when an isotopic substitution is made for atom A, such that its mass changes from m, to m, the vibrational frequency of A'-B, wAp can be expressed in terms of the vibrational frequency of A-B, @ An as o x=0 A (H/H", where u AB and u, are the effective masses of A-B and A'-B, respectively. (b) The vibrational frequency of 'HCl is 5.63 x 10"s". Calculate the vibrational frequency of (i) 'H*Cl and (ii) 'H"Cl. Use integer relative atomic masses. A'B
Transcribed Image Text:P7E.1 If the vibration of a diatomic A-B is modelled using a harmonic oscillator, the vibrational frequency is given by w=(k; /u)", where u is the effective mass, µ=m,m,/(m, +m,). If atom A is substituted by an isotope (for example H substituted for 'H), then to a good approximation the force constant remains the same. Why? (Hint: Is there any change in the number of charged species?) (a) Show that when an isotopic substitution is made for atom A, such that its mass changes from m, to m, the vibrational frequency of A'-B, wAp can be expressed in terms of the vibrational frequency of A-B, @ An as o x=0 A (H/H", where u AB and u, are the effective masses of A-B and A'-B, respectively. (b) The vibrational frequency of 'HCl is 5.63 x 10"s". Calculate the vibrational frequency of (i) 'H*Cl and (ii) 'H"Cl. Use integer relative atomic masses. A'B
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