Question

What is the wavelength of light that has a frequency of\[1.20{\text{ }} \times {\text{ }}{10^{13}}{\text{ }}{s^{ - 1}}\]?

Answer 1

Hint: The reason is, colours are nothing but electromagnetic radiations with a different wavelength of light. In the electromagnetic spectrum, the visible region is otherwise called visible light. These colours have different wavelengths too.


Formula used:
The relationship between frequency and wavelength for an electromagnetic wave is given by
\[c = f{\text{ }}\lambda \]———–(i)
Where,
$c$ is the velocity of light
$f$ is the frequency of light
$\lambda $ is the wavelength of the light

Complete step by step solution:
Wavelength is defined as the property of a wave in which the distance between the identical points between the two successive waves is calculated. It is denoted by the Greek letter lambda (λ). Therefore, the distance between either one crest or trough of one wave and the next wave is known as wavelength.
The wavelength of light is defined as “The distance between the two successive crests or troughs of the light wave”.
Wavelength of the Visible Light ranges between \[400{\text{ }}nm\]to \[700{\text{ }}nm\]and here we come to know the wavelength of various colours of the visible spectrum of light.
The spectrum of visible light has about numerous different colours having different wavelengths.
The violet colour is said to have the shortest form of wavelength whereas red colour is said to have the longest wavelength.
Frequency of the given light \[ = {\text{ }}f = {\text{ }}1.20{\text{ }} \times {\text{ }}{10^{13}}{\text{ }}{s^{ - 1}}\]
We need to find out the wavelength (λ) of the given light.
To find the wavelength of the given light we will substitute the known values in equation (i) we get,
\[c = f{\text{ }}\lambda \]
$c = 3 \times {10^8}m{s^{ - 1}}$
\[f = {\text{ }}1.20{\text{ }} \times {\text{ }}{10^{13}}{s^{ - 1}}\]
λ we need to find out
Therefore the equation becomes
\[\begin{array}{*{20}{l}}
  {3{\text{ }} \times {{10}^8} = {\text{ }}1.20{\text{ }} \times {\text{ }}{{10}^{13}} \times {\text{ }}\lambda } \\
  {\lambda = {\text{ }}3{\text{ }} \times {\text{ }}{{10}^8}{\text{ }}/{\text{ }}1.20{\text{ }} \times {\text{ }}{{10}^{13}}}
\end{array}\]
\[ = {\text{ }}2.5{\text{ }} \times {10^{ - 5m}}\]
Hence, the wavelength of light that has a frequency of \[1.20{\text{ }} \times {\text{ }}{10^{13}}{\text{ }}{s^{ - 1}}is{\text{ }}2.5{\text{ }} \times {\text{ }}{10^{ - 5m}}\]

Note: Wavelength can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave.