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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
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Capitolo 6, Problema 2b

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (b) Would the radiation produced by the appliance be visible to the human eye?
Diagram of the electromagnetic spectrum showing frequency ranges and visible light spectrum.

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Identify the frequency of the electromagnetic radiation produced by the kitchen appliance, which is 2450 MHz.
Convert the frequency from MHz to Hz by multiplying by 10^6 (since 1 MHz = 10^6 Hz).
Locate the frequency range of the visible spectrum on the electromagnetic spectrum diagram. The visible spectrum ranges from approximately 4 x 10^14 Hz to 7.5 x 10^14 Hz.
Compare the frequency of the kitchen appliance's radiation (2450 MHz or 2.45 x 10^9 Hz) to the frequency range of the visible spectrum.
Determine if the frequency of 2.45 x 10^9 Hz falls within the visible spectrum range. If it does not, then the radiation is not visible to the human eye.

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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by frequency or wavelength. It ranges from low-frequency radio waves to high-frequency gamma rays. The visible spectrum, which is the portion detectable by the human eye, lies between approximately 400 nm (violet) and 700 nm (red). Understanding where a specific frequency falls within this spectrum is crucial for determining its visibility.
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Electromagnetic Spectrum

Frequency and Wavelength

Frequency refers to the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). Wavelength is the distance between successive peaks of a wave, typically measured in nanometers (nm) for light. The relationship between frequency and wavelength is inversely proportional; as frequency increases, wavelength decreases. This relationship helps to categorize electromagnetic radiation into different types, including visible light.
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Frequency-Wavelength Relationship

Microwave Radiation

Microwave radiation is a type of electromagnetic radiation with frequencies ranging from about 300 MHz to 300 GHz, corresponding to wavelengths from 1 meter to 1 millimeter. The frequency of 2450 MHz, as mentioned in the question, falls within the microwave range. Microwaves are not visible to the human eye, as they lie outside the visible spectrum, which is essential for answering whether the radiation produced by the appliance is visible.
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Electromagnetic Radiation Example
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Domanda del libro di testo

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (d) Which of the following is the appliance likely to be? (i) A toaster oven, (ii) A microwave oven, or (iii) An electric hotplate.

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The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (a) What is the wavelength of such a sound wave?

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A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation.

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A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (c) If the radiation is not visible, do photons of this radiation have more or less energy than photons of visible light?

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Domanda del libro di testo

The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (b) What would be the frequency of electromagnetic radiation with the same wavelength?

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