The frequency of violet light with a wavelength of 420 nm is[tex]\boxed{7.14 \times {\text{1}}{{\text{0}}^{16}}{\text{ }}{{\text{s}}^{ - 1}}}[/tex].
Further explanation:
Wavelength is the characteristic property of a wave. It is defined as the distance between two successive crests or troughs. A crest is that point where there is maximum displacement of the medium whereas trough is a point that has minimum displacement of the medium. It is represented by [tex]\lambda[/tex] and its SI unit is meter (m).
Frequency is defined as the number of times n event occurs in unit time. It is generally applied to waves including light, sound and radio waves. It is denoted by [tex]{\nu }[/tex] and its SI unit is Hertz (Hz).
The formula to calculate the frequency of violet light is as follows:
[tex]\nu = \frac{c}{\lambda }[/tex] ...... (1)
Here,
c is the speed of violet light.
[tex]\nu[/tex] is the frequency of violet light.
[tex]\lambda[/tex] is the wavelength of violet light.
Firstly, the wavelength is to be converted into m. The conversion factor for this is,
[tex]{\text{1 nm}} = {10^{ - 9}}\;{\text{m}}[/tex]
So the wavelength of violet light can be calculated as follows:
[tex]\begin{aligned}\lambda&=\left({{\text{420 nm}}}\right)\left({\frac{{{{10}^{-9}}\;{\text{m}}}}{{{\text{1 nm}}}}}\right)\\&=4.2\times {10^{-9}}\;{\text{m}}\\\end{aligned}[/tex]
The value of the wavelength of violet light is [tex]4.2 \times {10^{ - 9}}\;{\text{m}}[/tex].
The value of the speed of violet light is [tex]3 \times {10^8}\;{\text{m/s}}[/tex].
Substitute these values in equation (1).
[tex]\begin{aligned}\nu&=\left({\frac{{3\times{{10}^8}\;{\text{m}}}}{{{\text{1 s}}}}} \right)\left( {\frac{1}{{4.2 \times {{10}^{-9}}\;{\text{m}}}}}\right)\\&=0.7142{\text{8}} \times {\text{1}}{{\text{0}}^{17}}{\text{ }}{{\text{s}}^{-1}}\\&=7.14\times {\text{1}}{{\text{0}}^{16}}{\text{ }}{{\text{s}}^{ - 1}} \\ \end{aligned}[/tex]
Learn more:
1. Statement about subatomic particle: https://brainly.com/question/3176193
2. The energy of a photon in light: https://brainly.com/question/7590814
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Structure of the atom
Keywords: wavelength, frequency, 420 nm, wavelength of violet light, speed of violet light, frequency of violet light, 3*10^8 m/s, 7.14*10^16 s-1, c, distance, crest, trough.
