Question

There are two categories of ultraviolet light. Ultraviolet A ( UVA ) has a wavelength ranging from 320 nm to 400 nm . It is not so harmful to the skin and is necessary for the production of vitamin D. UVB, with a wavelength between 280 nm and 320 nm , is much more dangerous, because it causes skin cancer.

Find the frequency ranges of UVA.
Enter your answers separated with commas.

Answer 1

`7.5x10^(14)Hz`,
`9.37x10^(14)Hz`.

Step-by-step explanation:

The ultraviolet light belongs to the electromagnetic spectrum.

The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities. That radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it.

Any radiation from the electromagnetic spectrum has a speed of
`3x10^(8)m/s` in vacuum.

Therefore, in order to know the frequency the following equation can be used:

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

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

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

Notice that it is necessary to express the wavelength in units of meters before it can be used in equation 2.

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

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

`\\u = 9.37x10^(14)s^(-1)`

But
`1Hz = s^(-1)`

`\\u = 9.37x10^(14)Hz`

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

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

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

Hence, the frequency range of UVA is
`7.5x10^(14)Hz` to
`9.37x10^(14)Hz`.