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Wave Optics

Question
CBSEENPH12039567
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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by straight U left parenthesis straight x right parenthesis space equals space straight a over straight x to the power of 12 minus straight b over straight x to the power of 16 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 = ∞) – Uat equilibrium], D is

  • b2/2a

  • b2/12a

  • b2/4a

  • b2/6a

Solution

C.

b2/4a

The potential energy for diatomic molecule is 
straight U left parenthesis straight x right parenthesis space equals space straight a over straight x to the power of 12 minus straight b over straight x to the power of 6 straight U space left parenthesis straight x space equals space infinity right parenthesis space equals space 0 As comma space straight F space equals space minus space dU over dx space equals space minus space open square brackets fraction numerator 12 straight a over denominator straight x to the power of 13 end fraction plus fraction numerator 6 straight b over denominator straight x to the power of 7 end fraction close square brackets At space equilibrium comma space straight F space equals space 0 therefore space straight x to the power of 6 space equals space fraction numerator 2 straight a over denominator straight b end fraction therefore space straight U subscript at space equilibrium end subscript space equals space straight a over open parentheses begin display style fraction numerator 2 straight a over denominator straight b end fraction end style close parentheses squared space minus space fraction numerator straight b over denominator open parentheses begin display style fraction numerator 2 straight a over denominator straight b end fraction end style close parentheses end fraction space equals space fraction numerator negative straight b squared over denominator 4 straight a end fraction therefore space straight D space equals space left square bracket space straight U space left parenthesis straight x equals space infinity right parenthesis minus straight U subscript at space equilibrium space right square bracket space end subscript space equals space fraction numerator straight b squared over denominator 4 straight a end fraction

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

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