What color might 600 nm be? I will address that in some problems to follow. Sometimes you might be asked what color a radiation might be. Visible light has a wavelegth somewhere between 400 and 700 nm. (x) (5.00 x 10 14 s¯ 1) = 3.00 x 10 8 m s¯ 1Ģ) By the way, the unit typically used for wavelengths of visible light is nanometers:Ħ.00 x 10¯ 7 m times (10 9 nm / 1 m) = 600 nm. Problem #7: Calculate the wavelength (in meters) of radiation a frequency of 5.00 x 10 14 s¯ 1. What is the wavelength of this frequency of light? Answer in units of nm. Problem #6: Light with a frequency of 7.26 x 10 14 Hz lies in the violet region of the visible spectrum. Given Frequency, Calculate Wavelength (five problems) However, 3.00 is good enough for introductory work. Also, the value for the speed of light is known to nine significant figures, as in 299,792,458 m s¯ 1. At an introductory level, you will not know this, so that is why I am telling you here. I choose to do this because I know wavelength measurements are very accurate and that 6, 7, or even 8 sig figs are possible. Note also that I effectively consider 7000 to be 4 significant figures. If I had done so, the value would have been 7.000 x 10¯ 5. Notice how I did not bother to convert 7000 x 10¯ 8 into scientific notation. This means you must remember that the conversion is 1 Å = 10¯ 8 cm. The solution below depends on converting Å into cm. Problem #5: What is the frequency of red light having a wavelength of 7000 Å? I didn't bother to put the wavelength in scientific notation. Problem #4: What is the frequency of infrared radiation of wavelength 67.5 μm?Ħ7.5 μm times (1 m / 10 6 μm) = 67.5 x 10 -6 mĢ) Use λν = c to determine the frequency: Problem #3: Calculate the frequency of electromagnetic radiation that has a wavelength of 1.315 micrometers.ġ.315 μm x (1 m / 10 6 μm) = 1.315 x 10¯ 6 m However, because of this, many teachers will be tempted to ask these types of problems using different units for the wavelength. The use of nm for wavelength is very common in science, almost standard usage. Calculate the frequency of this wavelength of electromagnetic radiation.Ĥ88 nm x (1 m / 10 9 nm) = 4.88 x 10¯ 7 m (4.42 x 10¯ 7 m) (x) = 3.00 x 10 8 m s¯ 1Įxample #2: The wavelength of an argon laser's output is 488.0 nm. Problem #1: Calculate the frequency of radiation with a wavelength of 442 nm.Ĥ42 nm x (1 m / 10 9 nm) = 4.42 x 10¯ 7 m Given Wavelength, Calculate Frequency (five problems) If you wish to review metric conversions, click here. Often, these problems require metric conversions. Sometimes a teacher might supply the centimeter value in the problem, but the meter value would be better suited for the solution. That being said, there are problems worded in such a way for which 3.00 x 10 10 cm s¯ 1 (for the speed of light) is the better-suited value. The reason for meters is that, to solve these type of problems, using 3.00 x 10 8 m s¯ 1 for the speed of light is usually the best choice. To solve these problems, you usually need to convert the wavelenth to meters before using λν = c. Problems #1 - 10 Wavelength-Frequency Problems #11 - 20 Go to Part Two of Light Equations Return to Part One of Light Equations Return to Electrons in Atoms menu Wavelength-Frequency Conversions Wavelength-Frequency Conversions
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