A particle is moving in one dimension between x a and x b and is described in

A particle is moving in one dimension between x a and

This preview shows page 2 out of 2 pages.

A particle is moving in one dimension between x = a and x= b , and is described in this region by a wavefunction ψ x ( ) = A / x , where A is a normalization constant. (a) Evaluate the normalization constant to ensure that the square of the wavefunction describes the probability distribution, P ( x ) of the particle. (b) Using the probability distribution, evaluate the mean value of the position of the particle. You should obtain x = ab b a ( ) ln b a ( ) 6. Modeling electrons in a molecule with the particle in a box. (a) A very simple model of an electron in a chemical bond is to imagine that it is approximately an electron in a box of a typical bondlength, such as 2 Å. Using the value, compute the energy difference between the ground (n=1) and excited (n=2) levels, in eV and kcal/mol. (b) Similarly one can model the 4 delocalized π electrons in a conjugated molecule, such as butadiene, C 4 H 6 , as occupying the particle in a box levels. Using the Aufbau principle, indicate which levels are occupied and then describe what levels are involved in the lowest energy excitation that is possible. Estimate the energy of this excitation (in eV) by making a reasonable definition of the length of the box. The particle in a box model has been used to understand the chain length dependence of the colors of dye molecules (though more accurate methods are now available!).
Image of page 2
  • Summer '16
  • Alistair Sinclair
  • Atom

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes