Ultraviolet light is typically divided into three categories. UV-A, with wavelengths between 400 nm and 320 nm, has been linked with malignant melanomas. UV-B radiation, which is the primary cause of sunburn and other skin cancers, has wavelengths between 320 nm and 280 nm. Finally, the region known as UV-C extends to wavelengths of 100 nm. (a) Find the range of frequencies for UV-B radiation. (b) In which of these three categories does radiation with a frequency of 7.9 * 1014 Hz belong

a) The UV-B has frequencies between and

b) The radiation with a frequency of belong to the UV-A category.

Explanation:

(a) Find the range of frequencies for UV-B radiation.

Ultraviolet light belongs to the electromagnetic spectrum, which distributes radiation along it in order of different frequencies or wavelengths.

Higher frequencies:  

Lower frequencies:

That radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it. Any of those radiations will have a speed of in vacuum.

The velocity of a wave can be determined by means of the following equation:

(1)  

Where c is the speed of light, is the frequency and is the wavelength.

Then, from equation 1 the frequency can be isolated.

(2)

Before using equation 2 to determine the range of UV-B it is necessary to express in units of meters in order to match with the units from c.

⇒

⇒

Hence, the UV-B has frequencies between and

(b) In which of these three categories does radiation with a frequency of belong.

The same approach followed in part A will be used to answer part B.

Case for UV-A:

⇒

Hence, the UV-A has frequencies between and .

Therefore, the radiation with a frequency of belongs to UV-A category.