## Introduction: 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.

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## Step 1: Things We Need

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

2. Chocolate bars (2 large)

3. Ruler

## Step 2: Place Chocolate Bars on the Turnable Plate

- 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.

## Step 3: Take Out the Chocolate From the Microwave

- 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.

## Step 4: Measure the Distance Between Consecutive Melted Spots

- 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**

## Step 5: Plugin the Numbers in the Formula V = F . Λ

- 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)

## Step 6: Enjoy the Results!

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!!

## 14 Discussions

4 years ago on Introduction

Great, but there is an easier way to demonstrate the speed of light: just leave any kid alone with it and see how fast it disappears :-)

Seriously though: well done

Reply 4 years ago on Introduction

:-) Thanks!

4 years ago

Absolutely wonderful!

Reply 4 years ago on Introduction

Thanks!

4 years ago

Simply Brilliant

Reply 4 years ago on Introduction

Thank you!

4 years ago on Introduction

Cool stuff and a great way to engage kids. Can you explain why the

v = f x λformula works?Reply 4 years ago on Introduction

Thanks!

SI units of speed is meter/second.

The speed of a wave (transverse) is the distance traveled by a given point on the wave (such as a crest or trough) in a given period of time.

The wavelength is measured in meters (m), from crest to crest (two consecutive points in the same phase=> one cycle) or trough to trough, so in the experiment measuredwavelength of the microwave radiation

, λ = 0.126 m

And wave frequency refers to the number of cycles occurring

per second, in the experiment frequency which is given on the oven, f = 2450M Hz, Hz (Hertz) means one cycle per second => Hz = 1 cycle/second

when we multiply λ and f, we get units of speed, m/s, =>

λ x f = 0.126 meter x 2450 x 10^6 /second => 0.126x2450x10^6

meter/second ~ 308700000 m/s = speedI hope I answered your question.Reply 4 years ago on Introduction

it does help. So does this mean that when dealing with a fixed speed like light that as the frequency slows down the wave length would get longer? For example, a frequency of 1 would yield a wave length that was one light second long.

Reply 4 years ago on Introduction

Yes!

shorter wavelength => higher frequency,

longer wavelength => less frequency,

(since

v = λ x f => λ = v/f, wavelength is inversely proportional to frequency).for

example, wavelength of gamma rays is very short, around 10^-11 m

therefore frequency is very high, around 10^20 Hz (or cycles per second)

and we consider radio waves, the wavelength is very long around 10^3 m

so the frequency is very less around 10^4 Hz.

For reference, please see attached image.

4 years ago on Introduction

This is great!! My kids are too young to understand the math part but we will do this anyway because teaching scientific thought is important at a young age especially when food is involved.

Reply 4 years ago on Introduction

Thanks!

4 years ago on Introduction

Cool science! I am glad you got to eat the chocolate too.

4 years ago

great work kid u are very cute nice