The potential energy function for the force between two atoms in … - Vidyadip

MCQ

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=$ $\;\frac{a}{{{x^{12}}}} - \frac{b}{{{x^6}}}$ where a and b are constants and $x $ is the distance between the atoms. If the dissociation energy of the molecule is $D = [ U ( x = \infty) - U_{ at\ equilibrium}], D$ is

A
$\frac{{{b^2}}}{{2a}}$
B
$\;\frac{{{b^2}}}{{6a}}$
✓
$\;\frac{{{b^2}}}{{4a}}$
D
$\;\frac{{{b^2}}}{{12a}}$

✓

Answer

Correct option: C.

$\;\frac{{{b^2}}}{{4a}}$

c
At equilibrium : $\frac{{dU(x)}}{{dx}} = 0$

$ \Rightarrow \frac{{ - 12a}}{{{x^{11}}}} = \frac{{ - 6a}}{{{x^5}}} \Rightarrow x = {\left( {\frac{{2a}}{b}} \right)^{\frac{1}{6}}}$

$\begin{gathered}
{U_{at}}\,equilibrium = \frac{a}{{{{\left( {\frac{{2a}}{b}} \right)}^2}}} - \frac{b}{{\left( {\frac{{2a}}{b}} \right)}} \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{b^2}}}{{a4}}\,and\,{U_{\left( {x = \infty } \right)}} = 0 \hfill \\
\end{gathered} $

$\therefore $ $D = 0$$ - \left( { - \frac{{{b^2}}}{{4a}}} \right) = \frac{{{b^2}}}{{4a}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 5.work,energy,power and collision→5.work,energy,power and collision — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The breaking stress of a wire depends upon

A perfect gas goes from state $A$ to another state $B$ by absorbing $8 \times {10^5}J$ of heat and doing $6.5 \times {10^5}J$ of external work. It is now transferred between the same two states in another process in which it absorbs ${10^5}J$ of heat. Then in the second process

Water is filled to a height $H$ behind a dam of width $w$. The resultant force on dam is ..............

The units of electrical permittivity are:

In a stationary wave,

All the particles of the medium vibrate in phase.
All the antinodes vibrate in phase.
The alternate antinodes vibrate in phase.
All the particles between consecutive nodes vibrate in phase.

A body of weight $50 \,N$ placed on a horizontal surface is just moved by a force of $28.2\, N$. The frictional force and the normal reaction are

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

Two trolley $A$ and $B$ are moving with accelerations $a$ and $2a$ respectively in the same direction. To an observer in trolley $A$ , the magnitude of pseudo force acting on a block of mass $m$ on the trolley $B$ is

Consider two ideal diatomic gases $\mathrm{A}$ and $\mathrm{B}$ at some temperature $T$. Molecules of the gas $A$ are rigid, and have a mass $m$. Molecules of the gas $\mathrm{B}$ have an additional vibrational mode, and have a mass $\frac{\mathrm{m}}{4} .$ The ratio of the specific heats $(\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}$ and $\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})$ of gas $\mathrm{A}$ and $\mathrm{B}$, respectively is

The angular speed of seconds needle in a mechanical watch is