Molecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3 U (r) = ¤ [(;)* - (;)*] . C (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with λ 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m' that represents the dynamical mass of the molecule. 4 = TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X = 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.
Molecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3 U (r) = ¤ [(;)* - (;)*] . C (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with λ 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m' that represents the dynamical mass of the molecule. 4 = TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X = 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.
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![Molecular Pair Potential
The vibrational properties of a diatomic molecule can often be described by Mie's
pair potential 3:
U(r) = C
c[9₁-9]
(4)
where U(r) is the potential energy between the two atoms, r is the distance between
the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with
X 12 is the Lennard-Jones potential and was covered in Lecture #2. For the
purposes of this problem, assume there is a mass ‘m’ that represents the dynamical
mass of the molecule. 4
TLTR:
(a) Find a combination of C, m, o that has the units of frequency.
(b) Derive the ratio of the equilibrium positions and of the frequencies of small
oscillations for X 10, 14. Show that the units for the equilibrium position and
for the frequency of the oscillations are consistent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd104ea5e-59f4-47a3-a0d3-8c9f1ad3b57c%2F68704900-d327-42b0-96a3-359658124517%2F14wjbl_processed.png&w=3840&q=75)
Transcribed Image Text:Molecular Pair Potential
The vibrational properties of a diatomic molecule can often be described by Mie's
pair potential 3:
U(r) = C
c[9₁-9]
(4)
where U(r) is the potential energy between the two atoms, r is the distance between
the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with
X 12 is the Lennard-Jones potential and was covered in Lecture #2. For the
purposes of this problem, assume there is a mass ‘m’ that represents the dynamical
mass of the molecule. 4
TLTR:
(a) Find a combination of C, m, o that has the units of frequency.
(b) Derive the ratio of the equilibrium positions and of the frequencies of small
oscillations for X 10, 14. Show that the units for the equilibrium position and
for the frequency of the oscillations are consistent.
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