d. For molecular nitrogen, the bond length is 1.1 x 10-1ºm, the bond (binding) energy is 9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for the interatomic potential? (Recall a = 2n times frequency in Hz)

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1. A model for the potential energy interaction between the two nitrogen atoms in the
N2 molecule is proposed that has the form:
v(4) = 4E, (4)* - ()']
12
a. Find the position of the potential minimum and its value there, in terms of o and Eo,
respectively. What do these parameters represent physically about the molecule?
b. Draw a hand sketch of V(r) showing rmin, V(rmin) and where V crosses the r axis.
c. If the atom is disturbed from its equilibrium by a small amount, show that the
7.56.
frequency of oscillation is w =
d. For molecular nitrogen, the bond length is 1.1 x 10-1°m, the bond (binding) energy is
9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy
laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for
the interatomic potential? (Recall o = 2n times frequency in Hz)
where m is the mass of a nitrogen atom.
Transcribed Image Text:1. A model for the potential energy interaction between the two nitrogen atoms in the N2 molecule is proposed that has the form: v(4) = 4E, (4)* - ()'] 12 a. Find the position of the potential minimum and its value there, in terms of o and Eo, respectively. What do these parameters represent physically about the molecule? b. Draw a hand sketch of V(r) showing rmin, V(rmin) and where V crosses the r axis. c. If the atom is disturbed from its equilibrium by a small amount, show that the 7.56. frequency of oscillation is w = d. For molecular nitrogen, the bond length is 1.1 x 10-1°m, the bond (binding) energy is 9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for the interatomic potential? (Recall o = 2n times frequency in Hz) where m is the mass of a nitrogen atom.
Expert Solution
Step 1

Given:

    Bond length, r= 1.1 x 10-10 m

    Bond energy, E= 9.79 eV = 15.66 x 10-19 J

    Mass, m = 14 amu = 23.38 x 10-27 kg

    Frequency, ν = 8.8 x 1013 Hz

   

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