Question

The frequency of the visible light of wavelength 6000 A$^o$ (Angstrom unit) is
\[\begin{align}
  & \text{A}\text{. }4\times {{10}^{14}}Hz \\
 & \text{B}\text{. }6000 \\
 & \text{C}\text{. }5\times {{10}^{10}}Hz \\
 & \text{D}\text{. }5\times {{10}^{14}}Hz \\
\end{align}\]

Answer 1

Hint: Frequency is the number of repeated events occurring per unit time. In terms of wavelength frequency is given as speed of light upon wavelength of light. By using this formula we can find the frequency of the visible light as wavelength is given and speed of light is a universal constant which we know.

Formula used:
\[f=\dfrac{c}{\lambda }\]

Complete answer:
The frequency is the number of waves passing at a particular interval of time. The frequency for the electromagnetic wave is given as
\[f=\dfrac{c}{\lambda }\]
The visible light lies in the electromagnetic spectra between the infrared region and the ultra-violet region and which is visible to the human eye and therefore it is named as visible light or visible region. Hence, we can calculate the frequency of the visible light by the above formula where c is the speed of light and its value is \[c=3\times {{10}^{8}}m/s\]

Substituting the value of λ
\[\begin{align}
  & \lambda =6000 A^o \\
 & \lambda =6000\times {{10}^{-10}}m \\
\end{align}\]

Then the frequency is given as
\[\begin{align}
  & f=\dfrac{3\times {{10}^{8}}}{6000\times {{10}^{-10}}}Hz \\
 & f=0.0005\times {{10}^{18}}Hz \\
 & f=5\times {{10}^{14}}Hz \\
\end{align}\]

So, the correct answer is “Option D”.

Additional Information:
Electromagnetic spectrum is the spectrum or the range of frequency of electromagnetic radiation. The electromagnetic spectrum consists of gamma ray, X-ray, ultraviolet, visible light, infrared, microwaves and radio waves. This is ordered from high frequency (or low wavelength) to low frequency (or high wavelength.)

Note:
The unit should be changed before substituting, like here the wavelength was given in A.U. and we changed into metre. The wavelength is also given in nanometres. If we didn’t change the unit properly the answer will be wrong. In general, the frequency is given by the same formula but speed of light is changed with the velocity.