Question

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

Answer 1

The ranges of frequency are:

UVA: $[7.50-9.38]\cdot 10^{14} Hz$

UVB: $[9.38-10.71]\cdot 10^{14} Hz$

Explanation:

The relationship between frequency and wavelength for an electromagnetic wave is the following:

$f = \frac{c}{\lambda}$

where

f is the frequency

$c=3.0\cdot 10^8 m/s$ is the speed of light

$\lambda$ is the wavelength

For the UVA, the range of wavelength is 320 nm - 400 nm, so

$\lambda_1 = 320 \cdot 10^{-9} m\\\lambda_2 = 400 \cdot 10^{-9} m$

So the corresponding frequencies are

$f_1 = \frac{3\cdot 10^8}{320\cdot 10^{-9}}=9.38\cdot 10^{14} Hz\\f_2= \frac{3\cdot 10^8}{400\cdot 10^{-9}}=7.50\cdot 10^{14} Hz$

For the UVB, the range of wavelength is 280 nm - 320 nm, so

$\lambda_1 = 280 \cdot 10^{-9} m\\\lambda_2 = 320 \cdot 10^{-9} m$

So the corresponding frequencies are

$f_1 = \frac{3\cdot 10^8}{280\cdot 10^{-9}}=1.07\cdot 10^{15} Hz\\f_2= \frac{3\cdot 10^8}{320\cdot 10^{-9}}=9.38\cdot 10^{14} Hz$

So the ranges of frequency are:

UVA: $[7.50-9.38]\cdot 10^{14} Hz$

UVB: $[9.38-10.71]\cdot 10^{14} Hz$

Learn more about waves, frequency and wavelength:

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