JEE MAIN - Physics (2022 - 24th June Evening Shift - No. 10)
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 :
$${\left( {{A \over B}} \right)^{{1 \over 5}}}$$
$${\left( {{B \over A}} \right)^{{1 \over 5}}}$$
$${\left( {{2A \over B}} \right)^{{1 \over 5}}}$$
$${\left( {{B \over 2A}} \right)^{{1 \over 5}}}$$
Explanation
For equilibrium
$$ - {{dU} \over {dr}} = 0 = {{10A} \over {{r^{11}}}} - {{5B} \over {{r^6}}}$$
$$ \Rightarrow {r^5} = {{2A} \over B}$$
And $$r = {\left( {{{2A} \over B}} \right)^{1/5}}$$
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