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4. One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance $r$, is $U(r) = U_0 \left[ \left( \frac{r_0}{r} \right)^{12} - \left( \frac{r_0}{r} \right)^6 \right]$ a. What units should $U_0$ and $r_0$ have? b. Sketch a graph of this potential energy function, assuming $r > 0$. c. Show that the distance between the atoms when the molecule is in stable equilibrium is given by $r_{eq} = 2^{1/6} r_0$ d. If the distance between the atoms increases from equilibrium to $r = 3^{1/6} r_0$. Show that the force from one atom on the other associated with this potential energy is given by $\vec{F} = -\frac{2U_0}{3^{7/6}r_0} \hat{r}$ e. Assume the atoms are oscillating so their maximum separation is the same as described in the previous part, $r_{max} = 3^{1/6} r_0$. This will be one of the turning points on your graph for the potential energy function. Go to the sketch you made in part (b.) and indicate this turning point as well as the other turning point on your graph.

          4. One model for the potential energy of a two-atom molecule, where the atoms are separated
by a distance $r$, is
$U(r) = U_0 \left[ \left( \frac{r_0}{r} \right)^{12} - \left( \frac{r_0}{r} \right)^6 \right]$
a. What units should $U_0$ and $r_0$ have?
b. Sketch a graph of this potential energy function, assuming $r > 0$.
c. Show that the distance between the atoms when the molecule is in stable equilibrium is
given by
$r_{eq} = 2^{1/6} r_0$
d. If the distance between the atoms increases from equilibrium to $r = 3^{1/6} r_0$. Show that the
force from one atom on the other associated with this potential energy is given by
$\vec{F} = -\frac{2U_0}{3^{7/6}r_0} \hat{r}$
e. Assume the atoms are oscillating so their maximum separation is the same as described in
the previous part, $r_{max} = 3^{1/6} r_0$. This will be one of the turning points on your graph for
the potential energy function. Go to the sketch you made in part (b.) and indicate this
turning point as well as the other turning point on your graph.

4. One model for the potential energy of a two-atom molecule, where the atoms are separated
by a distance r, is
U(r) = U0 [ ( (r0)/(r))^12 - ( (r0)/(r))^6 ]
a. What units should U0 and r0 have?
b. Sketch a graph of this potential energy function, assuming r > 0.
c. Show that the distance between the atoms when the molecule is in stable equilibrium is
given by
req = 2^1/6 r0
d. If the distance between the atoms increases from equilibrium to r = 3^1/6 r0. Show that the
force from one atom on the other associated with this potential energy is given by
F⃗ = -(2U0)/(3^7/6r0)r̂
e. Assume the atoms are oscillating so their maximum separation is the same as described in
the previous part, rmax = 3^1/6 r0. This will be one of the turning points on your graph for
the potential energy function. Go to the sketch you made in part (b.) and indicate this
turning point as well as the other turning point on your graph.

Added by Stephen V.

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