- #1
phys17
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Hi everyone,
Here is the question:
The mutual potential energy of a Li+ ion and an I- ion as a function of their separation r is expressed fairly well by the equation U(r)=(-Ke^2/r)+(A/r^10), where the first term arises from the Coulomb interaction, and the values of its constant are:
K= 9x10^9 N-m^2/C^2, e=1.6x10^-19 C
The equilibrium distance rnot between the centers of these ions in the LiI molecule is about 2.4 Angstrom. On the basis of this info,
(a) How much work in eV must be done to tear these ions completely away from each other?
(b) Taking the I- ion to be fixed b/c it is so massive, what is the frequency in Hz of the Li+ ion in vibrations of very small amplitude? Take the mass of Li+ as 10^/26
I used the U(r) formula to find the work, but how can you find the work without knowing what A is?
For part b, i found the second derivative of the U(r) function to get the value of the spring constant, k. Again, how do we know what the value of A is?
Thanks for any and all help!
Homework Statement
Here is the question:
The mutual potential energy of a Li+ ion and an I- ion as a function of their separation r is expressed fairly well by the equation U(r)=(-Ke^2/r)+(A/r^10), where the first term arises from the Coulomb interaction, and the values of its constant are:
K= 9x10^9 N-m^2/C^2, e=1.6x10^-19 C
The equilibrium distance rnot between the centers of these ions in the LiI molecule is about 2.4 Angstrom. On the basis of this info,
(a) How much work in eV must be done to tear these ions completely away from each other?
(b) Taking the I- ion to be fixed b/c it is so massive, what is the frequency in Hz of the Li+ ion in vibrations of very small amplitude? Take the mass of Li+ as 10^/26
The Attempt at a Solution
I used the U(r) formula to find the work, but how can you find the work without knowing what A is?
For part b, i found the second derivative of the U(r) function to get the value of the spring constant, k. Again, how do we know what the value of A is?
Thanks for any and all help!