Question

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

Answer 1

a) The UV-B has frequencies between
`9.375x10^(14)Hz` and
`1.071x10^(15)Hz`

b) The radiation with a frequency of
`7.9x10^(14)Hz` belong to the UV-A category.

Step-by-step 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:

• Gamma ray

• X ray

• Ultraviolet rays

• Visible region

Lower frequencies:

• Infrared

• Microwave

• Radio waves

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
`3x10^{8]m/s` in vacuum.

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

`c = \\u \cdot \lambda` (1)

Where c is the speed of light,
`\\u` is the frequency and
`\lambda` is the wavelength.

Then, from equation 1 the frequency can be isolated.

`\\u = (c)/(\lambda)` (2)

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

`\lambda = 320nm . (1m)/(1x10^(9)nm)` ⇒
`3.2x10^(-7)m`

`\lambda = 280nm . (1m)/(1x10^(9)nm)` ⇒
`2.8x10^(-7)m`

`\\u = (3x10^(8)m/s)/(3.2x10^(-7)m)`

`\\u = 9.375x10^(14)s^(-1)`

`\\u = 9.375x10^(14)Hz`

`\\u = (3x10^(8)m/s)/(2.8x10^(-7)m)`

`\\u = 1.071x10^(15)Hz`

Hence, the UV-B has frequencies between
`9.375x10^(14)Hz` and
`1.071x10^(15)Hz`

(b) In which of these three categories does radiation with a frequency of
`7.9x10^(14)Hz` belong.

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

Case for UV-A:

`\lambda = 400nm . (1m)/(1x10^(9)nm)` ⇒
`4x10^(-7)m`

`\\u = (3x10^(8)m/s)/(4x10^(-7)m)`

`\\u = 7.5x10^(14)s^(-1)`

`\\u = 7.5x10^(14)Hz`

Hence, the UV-A has frequencies between
`7.5x10^(14)Hz` and
`9.375x10^(14)Hz`.

Therefore, the radiation with a frequency of
`7.9x10^(14)Hz` belongs to UV-A category.