If the speed of light in a vacuum is approximately 3 x 10^8 m/s, what is the wavelength of light with a frequency of 6 x 10^14 Hz?

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Q: If the speed of light in a vacuum is approximately 3 x 10^8 m/s, what is the wavelength of light with a frequency of 6 x 10^14 Hz?

Solution: Using the formula c = fλ, where c = 3 x 10^8 m/s and f = 6 x 10^14 Hz. Thus, λ = c/f = (3 x 10^8)/(6 x 10^14) = 500 nm.

Steps: 6

Step 1: Understand the formula c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength.
Step 2: Identify the values given in the question: c = 3 x 10^8 m/s and f = 6 x 10^14 Hz.
Step 3: Rearrange the formula to solve for wavelength (λ): λ = c / f.
Step 4: Substitute the values into the formula: λ = (3 x 10^8 m/s) / (6 x 10^14 Hz).
Step 5: Perform the division: λ = 0.5 x 10^-6 m (which is the same as 500 nm).
Step 6: Convert the result to nanometers if needed: 1 meter = 1 x 10^9 nanometers, so 0.5 x 10^-6 m = 500 nm.