What is the frequency of radiation that has a wavelength of 13 \mu m, about the size of a bacterium?
To determine the frequency of radiation with a given wavelength, you can use the formula:
Frequency (f) = Speed of Light (c) / Wavelength (λ)
The speed of light is a constant value, approximately equal to 3 × 10^8 meters per second (m/s).
First, you need to convert the given wavelength of 13 μm to meters. Since 1 μm (micrometer) is equal to 1 × 10^(-6) meters, you can write the conversion as:
13 μm = 13 × 10^(-6) meters
Now, you can substitute these values into the frequency formula:
f = (3 × 10^8 m/s) / (13 × 10^(-6) m)
Next, simplify the expression:
f = (3 × 10^8) / (13 × 10^(-6)) = (3 × 10^8) * (10^6 / 13)
To make this calculation, multiply 3 × 10^8 by 10^6 and divide the result by 13:
f ≈ 23.08 × 10^14 Hz
Hence, the frequency of the radiation with a wavelength of 13 μm is approximately 23.08 × 10^14 Hz.