February 2018

Microwaving a chocolate bar

Robyn Ford, Region 10 Education Service Center, Richardson,Texas

Introduction

Why does one attend ChemEd? Welllll (good Texas word!), one just never knows what is going to be shared. At this year's ChemEd in Brookings, South Dakota, at South Dakota State University, we suffered from curiosity. The first author shared something she had read about¹ but was it really true? She had read that you can confirm the speed of light by microwaving a chocolate bar. Hmmm — this sounds like fun, so let's just do it! We got a couple of chocolate bars, called a few people to come investigate with us, and the rest is history. Although finding the speed of light is not in many chemistry curricula, we will call it a “good scientific” investigation, and it is perfect for Valentine's Day.

First to review, all electromagnetic waves, including microwaves, travel at the speed of light (3.00 x 10⁸ m/s) in a vacuum. We assumed the microwaves are traveling in a vacuum, although we would expect that the speed of microwaves in this setup would be lower because of the air and the chocolate.

In this experiment you can confirm the speed of light, but we decided to come from a different angle and use the known speed of light with our chocolate bar to confirm the reported frequency of the waves in our microwave oven.

Concepts

Understand the mathematical relationships between speed of light, frequency, wavelength and the energy of light
Calculate the frequency using the speed of light and wavelength: c =wavelength x speed of light
Calculate energy using Planck's constant, speed of light and wavelength

Materials (see Image 1)

Microwave oven (typically found in residential locations)
Chocolate bar (7 oz = 198 g, chocolate bar) at least 12 cm long. Microwaves cook by vibrating water molecules — will work on any and all chocolate bars!
Flat microwaveable tray to set chocolate bar on (keeps clean up to a minimum)
Ruler

chocolate

Image 1: Needed Supplies

Image 2: set up inside microwave

Preparation

Remove the turntable from the microwave oven — including the wheels if your microwave has them. Place microwaveable tray upside down over the center rotator in the oven and turn on for 5 s. (If the tray rotates, you might need to use a larger platform, like a paper plate.) You do not want your chocolate bar to move in the microwave. Put the chocolate bar upside down on the back of the tray (see Image 2).

Safety and disposal

No safety issues are associated with this activity. When the activity is finished, just consume any and all of the chocolate you want.

Engagement

View the following 3-minute YouTube experiment “Measure the Speed of Light — with Chocolate” uploaded by Jefferson labs (Thomas Jefferson National Accelerator Facility managed by Jefferson Science Associates, LLC for the U.S. Department of Energy).

Watch video on YouTube

Exploration

If you can confirm the speed of light (as described in the YouTube activity) by nuking a chocolate bar, you can also use this information to confirm the manufacturer's displayed frequency (see Image 3). According to the microwave oven specs, the reported frequency is 2450 MHz. How do you know if this is an accurate measurement? Can you validate this measurement?

Image 3: Microwave Specs

Place the chocolate bar upside down on the turned-over tray inside the microwave. Microwave for 15 s. Remove from oven and measure the distance between the melted "hot spots" on the chocolate bar. Provide calculated support for your confirmation using c = wavelength x speed of light.

Answer:

equation

Explanation

As all electromagnetic radiation, microwaves travel at the speed of light (c). A wavelength (l) is defined as the distance between two peaks (or two troughs) of the wave. Frequency (n) is measured in units per second (1/s = s^-1). The relationship found in the equation, c = l n, can be used to calculate the frequency. The distance between the two melted hot spots on the chocolate bar is considered to be one-half of a wavelength. Your measurement will need to be doubled to equal one wavelength.

Extension

Additional activities may include your choice of material to microwave, such as substances like marshmallows² and cheese.³ There are probably many other substances that could be used to track the hot spots that appear after microwaving for just a few seconds.

How long is a microwave? According to Wikipedia, the length of a microwave ranges between 1 m and 1 mm. How does the length of microwaves and the holes in the mesh screen of the microwave oven's door, which you can see through, compare? Why do microwaves not escape while the oven is operating?

Evaluation

Take your calculated frequency (e.g., 2459 MHz) and compare to the frequency published on your microwave. Determine the percentage of error in your measurement.
Given c = lxn and E = hxn, assuming identical frequencies, determine energy (E) in terms of the speed of light (c) and wavelength (l). Planck’s constant, h = 6.63 x 10⁻³⁴ J·s.

Answers

Extension: The electromagnetic waves used in a residential microwave oven are about 122 mm = 12.2 cm in length (Wikipedia). If the size of the holes in the metal mesh is less than 10 cm (actually the holes that are punched into the metal mesh are about 1-2 mm in diameter), then they are too small for the microwaves to escape providing a screen in which visible light (much smaller than the holes) can pass through allowing you to observe what is inside, but too small for microwaves to leak out.

equations