# Homework 12 (Due 5/4/16)

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.