if the frequency of a particular electromagnetic wave is 4 x 10^14 hertz, what is its wavelength of the radiation in nanometers (nm)?

To find the wavelength of a particular electromagnetic wave, you can use the equation:

wavelength (λ) = speed of light (c) / frequency (f)

The speed of light is a constant value, which is approximately 3 x 10^8 meters per second (m/s).

To convert the wavelength from meters (m) to nanometers (nm), you need to multiply the value by 10^9, since there are 10^9 nanometers in one meter.

Let's apply this formula to your question:

Given: frequency (f) = 4 x 10^14 hertz (Hz)

Step 1: Convert the frequency to meters per second (m/s)
f = 4 x 10^14 Hz

Step 2: Calculate the wavelength in meters (m)
λ = c / f
= (3 x 10^8 m/s) / (4 x 10^14 Hz)

Step 3: Convert the wavelength to nanometers (nm)
λ (in nm) = λ (in m) * (10^9 nm / 1 m)

Now, let's calculate the value:

λ = (3 x 10^8 m/s) / (4 x 10^14 Hz)
≈ 7.5 x 10^-7 meters (m)

λ (in nm) = 7.5 x 10^-7 m * (10^9 nm / 1 m)
≈ 750 nm

Therefore, the wavelength of the electromagnetic wave with a frequency of 4 x 10^14 Hz is approximately 750 nanometers (nm).