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Chemistry LibreTexts

Homework 12 (Due 5/4/16)

  • Page ID
    47389
  • Name: ______________________________

    Section: _____________________________

    Student ID#:__________________________

    Q12.1

    Calculate the wavelength associated with a 42 g baseball with speed of 80 m/s.

    Q12.2

    A typical mass for a horse is 510 kg, and a typical galloping speed is 22 kilometers per hour. Use these values to answer the following questions.

    1. What is the momentum of a galloping horse? What is its wavelength?
    2. If a galloping horse's velocity and position are simultaneously measured, and the velocity is measured to within ± 1.0%, what is the uncertainty of its position?
    3. Suppose Planck's constant was actually 0.01 J s. How would that change your answers to (a) and (b)? Which values would be unchanged?

    Hints:

    • de Broglie's postulate deals with the wave-like properties of particles.
    • Heisenberg's uncertainty principle deals with uncertainty of simultaneous measurements.

    Q12.3

    Draw the wave function for a particle in a box at the \(n = 4\) energy level.

    Q12.4

    Draw the probability distribution for a particle in a box at the \(n = 3\) energy level.

    Q12.5

    What is the probability of locating a particle of mass m between \(x = L/4\) and \(x = L/2\) in a 1-D box of length \(L\)? Assume the particle is in the \(n=1\) energy state.

    Q12.6

    Calculate the electronic transition energy of acetylaldehyde (the stuff that gives you a hangover) using the particle in a box model. Assume that aspirin is a box of length \(300 pm\) that contains 4 electrons.

    Q12.7

    Suggest where along the box the \(n=1\) to \(n=2\) electronic transition would most likely take place.