Question

Ultraviolet (UV) radiation is a part of the electromagnetic spectrum that reaches the Earth from the Sun. It has wavelengths shorter than those of visible light, making it invisible to the naked eye. These wavelengths are classified as UVA, UVB, or UVC, with UVA the longest of the three at 317 nm to 400 nm. Both the U.S. Department of Health and Human Services and the World Health Organization have identified UV as a proven human carcinogen. Many experts believe that, especially for fair-skinned people, UV radiation frequently plays a key role in melanoma, the deadliest form of skin cancer, which kills more than 8000 Americans each year. UVB has a wavelength between 280 nm and 317 nm. Determine the frequency ranges of UVA and UVB. UVA Hz (smaller value) Hz (larger value) UVB Hz (smaller value) Hz (larger value)

Answer 1

UVA:
`7.50\cdot 10^(14) Hz-9.46\cdot 10^(14) Hz`

UVB:
`9.46\cdot 10^(14) Hz-1.07\cdot 10^(15) Hz`

Step-by-step explanation:

The formula to calculate the frequency of each electromagnetic wave is:

`f=(c)/(\lambda)`

where

`c=3\cdot 10^8 m/s` is the speed of light

`\lambda` is the wavelength

For UVA:

- The minimum wavelength is

`\lambda=317 nm=3.17\cdot 10^(-7) m`

so the frequency is

`f=(c)/(\lambda)=(3\cdot 10^8 m/s)/(3.17\cdot 10^(-7) m)=9.46\cdot 10^(14) Hz`

- The maximum wavelength is

`\lambda=400 nm=4.00\cdot 10^(-7) m`

so the frequency is

`f=(c)/(\lambda)=(3\cdot 10^8 m/s)/(4.00\cdot 10^(-7) m)=7.50\cdot 10^(14) Hz`

For UVB:

- The minimum wavelength is

`\lambda=280 nm=2.80\cdot 10^(-7) m`

so the frequency is

`f=(c)/(\lambda)=(3\cdot 10^8 m/s)/(2.80\cdot 10^(-7) m)=1.07\cdot 10^(15) Hz`

- The maximum wavelength is

`\lambda=317 nm=3.17\cdot 10^(-7) m`

so the frequency is

`f=(c)/(\lambda)=(3\cdot 10^8 m/s)/(3.17\cdot 10^(-7) m)=9.46\cdot 10^(14) Hz`