$11.$A

$12.$D

$13.$B

I don't need help with $11.$ I just need help with number $12,$ am not getting the math and am getting a different answer than what it should be$.$ for $13$ I just need help knowing which chart to pick, please go into details about it

Chapter $2$ Atomic Structure and interatomic bonding:

$(4$ points$)$ The energy change $U(r)$ as a function of separation distance between

two atoms, $\text{'}r\text{'}$ is given as$,$

$U(r)=-\frac{A}{r^2}+\frac{B}{r^6}$

$11$ The distance $r_0$ at which $U(r)$ is minimized is given by:

a$.r_o=(\frac{3B}{A}{)}^{\frac{1}{4}}($answer$)$

b$.r_o=(\frac{3B}{A}{)}^{\frac{1}{2}}$

c$.r_0=(\frac{3A}{B}{)}^{\frac{1}{4}}$

d$.r_0=(\frac{3A}{B}{)}^{\frac{1}{2}}$

$12.(4$ points$)$ The energy $U(r)$ at distance $r_0$ is given by:

a$.U(r_0)=\frac{B^{\frac{3}{2}}}{\sqrt[\phantom{2}]{3A}}$

b$.U(r_0)=\frac{A^2}{\sqrt[\phantom{2}]{6B}}$

c$.U(r_0)=\frac{A^{\frac{3}{2}}}{\sqrt[\phantom{2}]{2B}}$

d$.U(r_0)=\frac{A^{\frac{3}{2}}}{\sqrt[\phantom{2}]{3B}}($answer$)$

$13(1$ point$)$ Choose the correct energy $(U(r))$ vs$.$ distance $r,$ diagram for bond $($answer is b but i don't know why. I would really appreciate a detail explanation about why it is this chart and how i would know to choose it$.$ thank you for your time and assistance in this problem.$)$