Question

Calculate the frequency of light that has a wavelength of \(75.0 \mathrm{~nm}\). What type of radiation is this?

Short answer

The frequency of the light is \(4.00 \times 10^{15}\) Hz, and it falls in the category of ultraviolet radiation.

Step-by-step solution

Understand and setup the formula.

The formula that relates the speed of light (\(c\)), the wavelength (\(\lambda\)), and the frequency (\(\nu\)) is \(c = \lambda \nu\). Also, understand that the speed of light (\(c\)) is approximately \(3.00 \times 10^8\) meters per second (m/s) and that we'll need to convert the wavelength from nanometers (nm) to meters (m) by multiplying by \(1.00 \times 10^{-9}\). Set up the conversion and the formula first.

Convert the wavelength.

Convert the wavelength from nanometers to meters. \(75.0 \mathrm{~nm}\) = \(75.0 \times 1.00 \times 10^{-9}\) meters = \(7.50 \times 10^{-8}\) meters.

Calculate the frequency.

Substitute the speed of light (\(c\)) and the wavelength (\(\lambda\)) into the formula \(c = \lambda \nu\). Rearrange the formula to solve for the frequency (\(\nu\)): \(\nu = \frac{c}{\lambda}\) = \(\frac{3.00 \times 10^8 \mathrm{~m/s}}{7.50 \times 10^{-8}\mathrm{~m}}\) = \(4.00 \times 10^{15}\) Hz (Hertz).

Identify the type of radiation.

Compare the obtained frequency with the range of frequencies for different types of electromagnetic radiation, and find out where it fits. In this case, a frequency of \(4.00 \times 10^{15}\) Hz falls in the range for ultraviolet radiation.