Question

A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. what is the highest frequency associated with this portion of the spectrum? (c = 3.00 × 108 m/s)

Answer 1

The lowest and highest wavelengths of this part of the electromagnetic spectrum are:
$\lambda_1 = 200 nm=200 \cdot 10^{-9} m$
$\lambda_2 = 400 nm=400 \cdot 10^{-9} m$

The frequency and the wavelenght of an electromagnetic wave are related by
$f= \frac{c}{\lambda}$
where c is the speed of light and f the frequency. By using this equation, we can find the frequencies that corresponds to the lowest and highest wavelengths of this part of the spectrum:
$f_1 = \frac{c}{\lambda_1}= \frac{3 \cdot 10^8 m/s}{200 \cdot 10^{-9} m}=1.5 \cdot 10^{15}Hz$
$f_2 = \frac{c}{\lambda_2}= \frac{3 \cdot 10^8 m/s}{400 \cdot 10^{-9} m}=7.5 \cdot 10^{14}Hz$

So, the highest frequency associated with this part of the spectrum is the one corresponding to the lowest wavelength:
$f_1 = 1.5 \cdot 10^{15}Hz$