Question

What is the frequency of blue light that has a wavelength of 463 nm?

Answer 1

Hint: We have to apply the relationship that exists between wavelength and frequency, where frequency and wavelength are inversely proportional to each other i.e. when wavelength increases frequency decreases and wavelength decreases and frequency increases.

Complete answer:
It is given in the question that wavelength () of blue light spectrum = 463 nm and speed of light (c) which is always constant = \[3\times {{10}^{8}}m/s\]
Now, we have to find the frequency of the blue light as we know that blue light comes under the visible spectrum. Visible spectrum is a small part of the electromagnetic spectrum. So its wavelength lies between 400nm-750 nm and its frequency lies between\[4\times {{10}^{14}}-7.5\times {{10}^{14}}hz\].
Electromagnetic spectrum should contain various waves with shorter or small wavelengths and higher (Large) frequencies which include ultraviolet light rays, X-rays, and gamma rays. Electromagnetic waves also have longer wavelength waves and lower frequencies which includes infrared light, microwaves, and radio and television waves.
Under visible spectrum different colours are obtained they are Violet, Indigo, Blue, Green, Yellow, Orange and red. In these colours violet and indigo are not dominant to our eyes.
Since frequency of visible spectrum lies between\[4\times {{10}^{14}}-7.5\times {{10}^{14}}hz\].
Now we should apply the formula,
\[speed=\dfrac{distance}{time}\]
Here in this question speed is the speed of light in vacuum and air, distance is the wavelength and time is the time period of the wave.
Since, we know that
\[time period=\dfrac{1}{frequency}\]
So, the equation can be rewritten as
Speed of light = wavelength frequency
Now according to the relation,
\[c=\lambda f\]
\[\therefore f=\dfrac{c}{\lambda }\]
First, we need to convert nm into m (1nm= 10-9m)
So, 463nm we get converted to 463 10-9m
Put these values in above equation we get
\[f=\dfrac{3.00\times {{10}^{8}}m/s}{463\times {{10}^{-9}}m}\]
\[\therefore f=6.48\times {{10}^{14}}Hz\]
So this is the required value of frequency of blue light. Now we can see that our answer lies in the given range of visible spectrum.

Note:
We must take care of the units as they may lead you to wrong answers. For the relationship told mathematically, if the speed of light is in m/s, the wavelength must be in meters and the frequency in Hertz Here (463 nm=463 10-9 m).Conversion of units will be done carefully.