The wavelength of some violet light is 420.0 nm. what is the frequency of this violet light?
The equation relating wavelength and frequency of light is:
v = fλ; where v is the wave's speed, f is its frequency and λ is the wavelength.
The speed of violet light will be the same as for any elecromagnetic radiation, that is,
3 x 10⁸ m/s
3 x 10⁸ = f(420 x 10⁻⁹)
f = 7.14 x 10¹⁴ Hz
The frequency of light for which the wavelength is \(420\,{\text{nm}}\)is \(\boxed{7.14 \times {{10}^{14}}\,{\text{Hz}}}\).
Further explanation:
The frequency is a measure of number of wave’s that passes through a fixed point or place in a given time interval. The S.I unit of frequency is Hertz \(\left( {{\text{Hz}}} \right)\).
Wavelength is defined as the distance between two successive crests or troughs of a travelling wave.
Examples of waves are sound wave, light wave, mechanical waves, surface waves etc.
Given:
The wavelength of the light used is \(420\,{\text{nm}}\).
The speed of the light is \(3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-
ulldelimiterspace} {\text{s}}}\).
Concept:
Light is an electromagnetic wave which carries energy in the form of electric field and magnetic field. The speed of light in vacuum is \(3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-
ulldelimiterspace} {\text{s}}}\).
The speed of light can be expressed in terms of wavelength of the light and the frequency of the light.
The speed of light is:
\(c = f \cdot \lambda\)
Rearrange the above expression.
\(\boxed{f=\frac{c}{\lambda }}\) …… (1)
Here, \(f\) is the frequency of the light, \(c\) is the speed of the light in vacuum and \(\lambda\) is the wavelength of the light.
Substitute \(3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern- ulldelimiterspace} {\text{s}}}\) for \(c\) and \(420 \times {10^{ - 9}}\,{\text{m}}\) for \(\lambda\) in equation (1).
\(\begin{aligned}f&=\frac{{3\times{{10}^8}\,{{\text{m}}\mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}}\right.\kern- ulldelimiterspace}{\text{s}}}}}{{420 \times {{10}^{-9}}\,{\text{m}}}}\\&=7.14\times {10^{14}}\,{\text{Hz}} \\ \end{aligned}\)
Thus, the frequency of light for which the wavelength is \(420\,{\text{nm}}\)is \(\boxed{7.14 \times {{10}^{14}}\,{\text{Hz}}}\).
Learn More:
1. What is the threshold frequency ν0 of cesium? Note that 1 ev (electron volt)=1.60×10−19 j. Https://brainly.com/question/6953278
2. Calculate the wavelength of an electron (m = 9.11 × 10-28 g) moving at 3.66 × 106 m/s https://brainly.com/question/1979815
3. What is the frequency of light for which the wavelength is 7.1 × 102 nm https://brainly.com/question/9559140
Answer Details:
Grade: High School
Subject: Physics
Chapter: Electromagnetic Waves
Keywords:
Frequency, light, wavelength, 420 nm, 4.20x10^-7 m, 7.14x10^14 Hz, vacuum, air, crests, troughs, sound wave, light wave, mechanical wave.
