Wavelength and Frequency Microwaves that heat food in a home microwave oven have a frequency of [latex]2.45 × 10^9 s^{-1}[/latex]. Calculate the wavelength of this radiation in nanometers, nm.

[latex]1.22 × 10^8 nm[/latex] Strategy and Explanation Rearrange the equation relating frequency, the speed of light, and wavelength to calculate the wavelength of this radiation. Recall that [latex]1 m = 1 × 10^9 nm[/latex]. [latex]λ = \frac{c}{v} = \frac{2.998 × 10^8 m/s}{2.45 × 10^9 s^{-1}} = 0.122 m[/latex] Convert meters to nanometers: [latex]0.122 m × \frac{1 × 10^9 nm}{1 m} = 1.22 × 10^8 nm[/latex] Reasonable Answer Check Compare the calculated wavelength (0.122 m) with the wavelength of the microwave region of the electromagnetic spectrum illustrated in Figure 7.1. The calculated wavelength falls within the microwave region and thus the answer is reasonable.

Question 7.PS.1: Wavelength and Frequency Microwaves that heat food in a home......

Principles of Chemistry The Molecular Science [1096176]

Wavelength and Frequency

Microwaves that heat food in a home microwave oven have a frequency of $2.45 × 10^9 s^{-1}$ . Calculate the wavelength of this radiation in nanometers, nm.

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1.22 \times 10^8 nm

Strategy and Explanation Rearrange the equation relating frequency, the speed of light, and wavelength to calculate the wavelength of this radiation. Recall that $1 m = 1 \times 10^9 nm$ .

$λ = \frac{c}{v} = \frac{2.998 × 10^8 m/s}{2.45 × 10^9 s^{-1}} = 0.122 m$

Convert meters to nanometers:

$0.122 m × \frac{1 × 10^9 nm}{1 m} = 1.22 × 10^8 nm$

Reasonable Answer Check Compare the calculated wavelength (0.122 m) with the wavelength of the microwave region of the electromagnetic spectrum illustrated in Figure 7.1. The calculated wavelength falls within the microwave region and thus the answer is reasonable.