Question

What is the wavelength of light (nm) that has a frequency of 6.44 x 1013 s-1?

Answer 1

The wavelength of the wave of light having the frequency of  $6.44 \times {10^{13}}\,{\text{Hz}}$ will be $\boxed{4.658 \times {{10}^{ - 6}}\,{\text{m}}}$ or  $\boxed{4658\,{\text{nm}}}$.

Further Explanation:

Given:

The frequency of the light is  $6.44 \times {10^{13}}\,{\text{Hz}}$.

Concept:

The light wave is an electromagnetic wave. An electromagnetic wave is a transverse wave. All the electromagnetic waves having different frequencies and wavelength are considered to be moving at the speed of light.

The transverse waves are the waves in which the direction of vibration of the medium particle is perpendicular to the propagation of the wave.

The light rays are called as the electromagnetic waves because they have the electric field as well as the magnetic field oscillating perpendicular to each other and also perpendicular to the direction of propagation of the wave.

The relation between the wavelength of the electromagnetic waves and its frequency is:

$\boxed{\lambda=\frac{c}{f}}$

Here, $\lambda$ is the wavelength, $c$ is the speed of light and $f$ is the frequency of the light.

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

Substitute the values in above expression.

$\begin{aligned}\lambda&= \frac{{3 \times {{10}^8}}}{{6.44 \times {{10}^{13}}}}\,{\text{m}}\\&= 4.{\text{658}}\times {\text{1}}{{\text{0}}^{ - 6}}\,{\text{m}}\\&= 4658\,{\text{nm}}\\\end{aligned}$

Thus, the wavelength of the wave of light having the frequency of $6.44\times {10^{13}}\,{\text{Hz}}$ will be $\boxed{4.658 \times {{10}^{ - 6}}\,{\text{m}}}$ or $\boxed{4658\,{\text{nm}}}$

Learn More:

1. Which of the following statements is a consequence of the equation e = mc2 brainly.com/question/2321496

2. What is the frequency of light for which the wavelength is 7.1 × 102 nm brainly.com/question/9559140

3. A radio station's channel, such as 100.7 fm or 92.3 fm, is actually its frequency in megahertz (mhz), where 1mhz=106hz and 1hz=1s−1 brainly.com/question/9527365

Answer Details:

Grade: High School

Subject: Physics

Chapter: Electromagnetic waves

Keywords:  Wavelength, frequency, electromagnetic waves, transverse waves, light wave, electric and magnetic field, oscillating perpendicular, 6.44 x 10^13 Hz.

Answer 2

4660

Hope this helped!
STSN