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Chapter 7: Problem 153

A student placed a large unwrapped chocolate bar in a microwave oven without a rotating glass plate. After turning the oven on for less than a minute, she noticed there were evenly spaced dents (due to melting) about \(6 \mathrm{~cm}\) apart. Based on her observations, calculate the speed of light given that the microwave frequency is \(2.45 \mathrm{GHz}\). (Hint: The energy of a wave is proportional to the square of its amplitude.)

Short Answer

Expert verified
The calculated speed of light, based on the observations made with the microwave oven and the chocolate bar, is approximately \(294,000,000 m/s\). This is close to the widely accepted scientific value of \(299,792,458 m/s\), thus validating the experiment conducted with the microwave oven.

Step by step solution

01

Convert frequency from GHz to Hz

The given frequency of the microwaves is 2.45 GHz. However, in scientific calculations, it is more common to use Hz (Hertz) as the unit of frequency. This requires us to convert 2.45 GHz to Hz by using the conversion factor \(1 GHz = 10^{9} Hz\). So, \(f = 2.45 GHz = 2.45 * 10^{9} Hz\).
02

Determine the wavelength

The dents in the chocolate bar, due to the melting, occurred at uniformly spaced intervals of 6 cm. The distance between peaks (or troughs) of a wave is the wavelength. Therefore, the wavelength \(\lambda\) of the microwaves is twice the distance between the melting spots, as one full wave includes a peak and a trough. So, \(\lambda = 2 * 6 cm = 12 cm = 0.12 m\). The conversion from cm to m is necessary to keep the units consistent.
03

Calculate the speed of light

The speed of light (\(c\)) can now be calculated using the formula \(c = \lambda f\). Plug in the values for the calculated wavelength (\(\lambda\)) and the converted frequency (\(f\)), \(c = 0.12 m * 2.45 * 10^{9} Hz = 294,000,000 m/s\).

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Most popular questions from this chapter

A photoelectric experiment was performed by separately shining a laser at \(450 \mathrm{nm}\) (blue light) and a laser at \(560 \mathrm{nm}\) (yellow light) on a clean metal surface and measuring the number and kinetic energy of the ejected electrons. Which light would generate more electrons? Which light would eject electrons with greater kinetic energy? Assume that the same amount of energy is delivered to the metal surface by each laser and that the frequencies of the laser lights exceed the threshold frequency.

Which orbital in each of the following pairs is lower in energy in a many- electron atom? (a) \(2 s, 2 p ;\) (b) \(3 p, 3 d ;\) (c) \(3 s, 4 s ;\) (d) \(4 d, 5 f\)

Define the following terms and give an example of each: transition metals, lanthanides, actinides.

What is meant by the term "shielding of electrons" in an atom? Using the \(\mathrm{Li}\) atom as an example, describe the effect of shielding on the energy of electrons in an atom.

Explain the statement, Matter and radiation have a "dual nature."
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