Respuesta :
The wavelength of light (ʎ) and the frequency (f) has the following relationship:
ʎ = c / f
where c is the speed of light, therefore:
ʎ = (3 x 10^8 m/s ) / 6.44 × 10^13 s-1
ʎ = 4.66 x 10^-6 m = 4.66 x 10^3 nm
The wavelength of the light having a frequency of [tex]6.44\times{10^{13}}\,{\text{Hz}}[/tex] is [tex]\boxed{4.66\times{{10}^{-6}}\,{\text{m}}}[/tex] or [tex]\boxed{466\,{\text{nm}}}[/tex] .
Further Explanation:
The light waves are the electromagnetic waves which can travel either in space or in medium. The electromagnetic waves are the transverse waves.
In transverse waves, the oscillation of the medium particle is perpendicular to the direction of propagation of the wave.
All the electromagnetic waves having different frequencies and wavelength are considered to move at the speed of light. The speed of the light moving through the space or air is [tex]3\times{10^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}[/tex] .
The relation between the wavelength of a wave with the speed of the light and the frequency of the wave is given as:
[tex]\boxed{\lambda =\frac{c}{f}}[/tex]
Substitute the value of [tex]c[/tex] and [tex]f[/tex] in above expression.
[tex]\begin{aligned}\lambda&=\frac{{3\times{{10}^8}}}{{6.44\times{{10}^{13}}}}\\&=4.658\times{10^{-6}}\,{\text{m}}\\&\approx{\text{4}}{\text{.66}}\times{\text{1}}{{\text{0}}^{-6}}\,{\text{m}}\\&\approx{\text{466}}\,{\text{nm}}\\\end{aligned}[/tex]
Thus, the wavelength of the light having a frequency of [tex]6.44\times{10^{13}}\,{\text{Hz}}[/tex] is [tex]\boxed{4.66\times{{10}^{-6}}\,{\text{m}}}[/tex] or [tex]\boxed{466\,{\text{nm}}}[/tex] .
Learn More:
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Electromagnetic Waves
Keywords:
Wavelength of light, frequency, speed of light, electromagnetic waves, transverse wave, perpendicular, direction of propagation, f=6.44x10^13 Hz.
