Question

The wavelength of some violet light is 420.0 nm. what is the frequency of this violet light?

Answer 1

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 $3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}$.

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 $3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}$.

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 $3 \times {10^8}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}$ for $c$ and $420 \times {10^{ - 9}}\,{\text{m}}$ for $\lambda$ in equation (1).

$\begin{aligned}f&=\frac{{3\times{{10}^8}\,{{\text{m}}\mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}}{{420 \times {{10}^{-9}}\,{\text{m}}}}\\&=7.14\times {10^{14}}\,{\text{Hz}} \\ \end{aligned}$

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. brainly.com/question/6953278

2. Calculate the wavelength of an electron (m = 9.11 × 10-28 g) moving at 3.66 × 106 m/s brainly.com/question/1979815

3. What is the frequency of light for which the wavelength is 7.1 × 102 nm 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.

Answer 2

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