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Chapter 8: Problem 5

Without doing detailed calculations, determine which of the following wavelengths represents light of the highest frequency: (a) \(6.7 \times 10^{-4} \mathrm{cm} ;\) (b) \(1.23 \mathrm{mm}\) (c) \(80 \mathrm{nm} ;\) (d) \(6.72 \mu \mathrm{m}\)

Short Answer

Expert verified
The shortest wavelength corresponds to the highest frequency. In this case, the wavelength of \(80 nm\) is the shortest, so light with this wavelength has the highest frequency.

Step by step solution

01

Understand Units

Identify the units used and convert all into the same unit for easy comparison. Here, the smallest unit nanometer (nm) could be chosen as the standard.
02

Unit Conversion

Convert all the units into nanometers. (a) To convert centimeters to nanometers, multiply by \(1 \times 10^{7}\). So, \(6.7 \times 10^{-4} cm = 6.7 \times 10^{3} nm. (b) To convert millimeters to nanometers, multiply by \(1 \times 10^{6} \). So, \(1.23 mm = 1.23 \times 10^{6} nm. (c) Is already in the unit nm. (d) To convert micrometers to nanometers, multiply by \(1 \times 10^{3} \). So, \(6.72 \mu m = 6.72 \times 10^{3} nm.\)
03

Comparision

Now that all the wavelengths are in the same unit, compare them to find out which one is the shortest. The shortest wavelength will represent light of the highest frequency.

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