Kitchen Physics - Measure the Speed of Light With Chocolate!

In honor of the International Year of Light, my 6 year old daughter calculates the speed of light using chocolate bars and microwave oven.

Microwaves are part of light or electromagnetic spectrum. We have been
using this radiation in microwave ovens to heat up the food for the past 50 years or so.

Image: http://planck.cf.ac.uk/science/mm-wave-astronomy

Safety & Precautions:
THIS EXPERIMENT SHOULD ONLY BE PERFORMED UNDER THE SUPERVISION OF AN ADULT.

1. Microwave oven (1100W, Frequency f = 2450MHz => 2450 million cycles per second)

2. Chocolate bars (2 large)

3. Ruler

• Remove the turnable roller ring under the plate in the microwave oven. Put the plate back inside the oven so that the plate won't rotate when using it.
• put two chocolate bars on the microwave plate next to one another.
• close the door and run the microwave oven for 25-35 seconds.

• Take out the plate from the microwave oven and you will find hot and cold spots on the chocolate bars because of standing microwaves.

• Chocolate will melt at crest (peak) and trough (valley) of the standing waves as more energy is concentrated at these places.

• Now take a ruler and measure the distance between two consecutive melted spots on the chocolate and note down the length on a piece of paper.

• In our case the distance between two melted points is, L = 6.3 cm = 0.063m, this length is half of the wavelength (λ).

• λ/2 = L= 0.063 m, therefore λ = 2L = 2*(0.063) m => λ = 0.126 m

• Now, we calculated the wavelength of the microwave radiation, λ = 0.126 m

• The frequency (f) of the microwave will be given on the oven and in the previous step we found wavelength (λ) by measuring the distance between two consecutive melting points on the chocolate.

• frequency of the microwave = 2450 million cycles per second = 2450 MHz

• f = 2450 x 10^6 Hz

• λ = 0.126 meters

• speed of the microwave radiation = frequency x wavelength

• v = f x λ

Now plug in f & λ values in the above formula

v = 2450MHz x 0.126 m

v = 2450 x 0.126 x 10^6 m/s

• v = 308700000 m/s
  

According to National Institute of Standards and Technology (NIST), the speed of light in the vacuum is,

c = 299792458 m/s

Now let us estimate the error in our measurement,

percent error = [ |measured value - actual value| / (actual value) ] * 100%

percent error = [|308700000 - 299792458| / 299792458] * 100%

• percent error ~ 2.9% (not bad)

After doing the experiment and analysis of the data, just enjoy your speed of the light result by eating the delicious melted chocolate.

Science is fun and yummy!!