# 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.

- What is the momentum of a galloping horse? What is its wavelength?
- 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?
- 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.