Question

Visible spectrum contains light of the following colours “Violet-Indigo-Blue-Green-Yellow-Orange-Red” (VIBGYOR). It’s frequency ranges from Violet (\[7.5 \times {10^{14}}\]Hz) to Red (\[4 \times {10^{14}}\]Hz). Find out maximum wavelength in this range.
A. \[400\;\mathop {\rm{A}}\limits^{\rm{o}} \]
B. \[750\mathop {\;{\rm{A}}}\limits^{\rm{o}} \]
C. \[4000\mathop {\;{\rm{A}}}\limits^{\rm{o}} \]
D. \[7500\;\mathop {\rm{A}}\limits^{\rm{o}} \]

Answer 1

Hint: We know that visible light spectrum is the part of the electromagnetic spectrum that the human eye can view. This range of wavelengths is called visible light. The human eye can detect wavelengths from 380 to 700 nanometers. All the seven colour lights have different frequencies. The frequency of light decreases from violet to red, hence, wavelength increases from violet to red.

Step by step answer: So from the question red light has the lowest frequency, we know that wavelength is inversely proportional to the frequency. It means when frequency increases then wavelength decreases, and when wavelength increases the frequency decreases. Therefore, the maximum wavelength is calculated in this region.
We know the relation between the frequency, wavelength, and speed of light. Where c is speed of light, v is frequency and \[\lambda \] is the wavelength of light.
\[\lambda = \dfrac{c}{v}\]
Now, substituting the given values in the above formula, we can calculate the value of wavelength.
We know that the Si unit of Hz is \[{{\rm{s}}^{ - 1}}\]
\[\begin{array}{c}
\lambda = \dfrac{{3 \times {{10}^8}\;{\rm{m/s}}}}{{4 \times {{10}^{14}}{{\rm{s}}^{ - 1}}}}\\
 = 7500 \times {10^{ - 10}}\;{\rm{m}}\\
1\mathop {\;{\rm{A}}}\limits^{\rm{o}} = {10^{ - 10}}\;{\rm{m}}
\end{array}\]

Therefore, the correct answer is (D).

Note: Visible light is visible because most of the gases in planetary atmospheres are transparent. To those wavelengths, in visible spectrum red light has maximum visibility. The Rayleigh scattering of a colour is inversely proportional to the fourth power of wavelength of that colour. Due to its large wavelength (of range 780-622nm) red colour scatters the least amongst all colours.