Download App

5.work,energy,power and collision — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
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

Bernoulli's theorem is based on conservation of:
→
The equation E = pc is valid:
→
The fundamental unit which has the same power in the dimension formula of surface tension and viscosity is
→
At temperature $T$ , the power radiated by a body is $Q$ watts. At the temperature $3T$ the power radiated by it will be
→
Two stones having different masses $m_1$ and $m_2$ are projected at an angle $\alpha$ and $\left(90^{\circ}-\alpha\right)$ with same speed from same point. The ratio of their maximum heights is
→
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is $5\,cm$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, in $cm,$ will be
→
In a stationary wave,
  1. All the particles of the medium vibrate in phase.
  2. All the antinodes vibrate in phase.
  3. The alternate antinodes vibrate in phase.
  4. All the particles between consecutive nodes vibrate in phase.
→
A ball is projected upwards from a height $h$ above the surface of the earth with velocity $v$. The time at which the ball strikes the ground is
→
One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the  length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it  vibrates in resonance in its simplest standing-wave vibration state. Determine the  relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.
→
The surface tension of a liquid at its boiling point:
→