Question

The wavelength range of the visible spectrum extends from violet $\left(400nm\right)\text{to red}\left(750nm\right).$ Express these wavelengths in frequencies $\left(H_Z\right).(1nm={10}^{-9}m)$

Answer 1

We know that $\lambda =\frac{c}{v}\text{or}v=\frac{c}{\lambda }$

$c=$ speed of electromagnetic radiation
$v=$ frequency
$\lambda =$ wavelength

Convert wavelength to frequency
Frequency of violet light,

$v=\frac{c}{\lambda }=\frac{3\times {10}^{8}ms-1}{400\times {10}^{-9}m}=7.50\times {10}^{14}{H}_Z$

Frequency of red light

$v=\frac{c}{\lambda }=\frac{3\times {10}^{8}m{s}^{-1}}{750\times {10}^{-9}m}=4.00\times {10}^{14}{H}_Z$

So, the range of visible spectrum is from $4.0\times {10}^{14}\text{to}7.50\times {10}^{14}{H}_Z$ in terms of frequency.

Final answer: $4\times {10}^{14}-7.5\times {10}^{14}{H}_Z$