Why Is My Wavelength Calculation Incorrect?

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The discussion centers on calculating the wavelength of an electromagnetic wave with a frequency of 7x10^19 Hz in free space, using the speed of light at 2.99792x10^8 m/s. The initial calculation incorrectly applied the relationship between frequency and wavelength, leading to an erroneous result of 1.467X10^12. The correct formula to use is c = fλ, where frequency is in Hz and wavelength is in meters. It's emphasized that wavelength should not be confused with wave number, which is defined differently. The correct approach to find the wavelength involves using the proper units and relationships in wave equations.
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What is the wavelength, k, corresponding to a frequency, w, of 7x10^19 Hz of electromagnetic wave in free space? The speed of light is 2.99792x10^8 m/s. Answer in units of m.
I set w/k=c
Plugging in (2*pi*7X10^19) for w, and 2.99792x10^8 for c, I got 1.467X10^12. The answer is wrong. Where did I go wrong?
 
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For one thing, the wave equation is c = f \lambda. The frequency is in given in Hz; the wavelength (not wave number) has units of meters.

PS: Don't confuse wavelength with the wave number (k), which is generally defined as k = 2 \pi / \lambda. If you want the wave number, then using k = \omega / c will work.
 
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