Question 109: Properties of Matter

Question

Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

Accepted Answer

For equilibrium
$$ - {{dU} \over {dr}} = 0 = {{10A} \over {{r^{11}}}} - {{5B} \over {{r^6}}}$$
$$ \Rightarrow {r^5} = {{2A} \over B}$$
And $$r = {\left( {{{2A} \over B}} \right)^{1/5}}$$

Answer

$${\left( {{A \over B}} \right)^{{1 \over 5}}}$$

Answer

$${\left( {{B \over A}} \right)^{{1 \over 5}}}$$

Answer

$${\left( {{2A \over B}} \right)^{{1 \over 5}}}$$

Answer

$${\left( {{B \over 2A}} \right)^{{1 \over 5}}}$$

Properties of Matter

Potential energy as a function of r is given by $U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

Choose the correct answer: