Question

The wavelength of some yellow light is 580.0 nm. What is the frequency of this yellow light?

Answer 1

The frequency of yellow light of wavelength 580 nm is  $\boxed{{0.05172\times10^{18}}\text{Hz}}$

Further Explanation:

Wavelength is the characteristic property of a wave. The term wavelength is defined as the distance between two successive crests or troughs in a wave. It is represented by $\lambda$ and its SI unit is meter (m).

The term 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 ${\text{v }}$ and its SI unit is Hertz (Hz).

The conversion factor to convert nm to m is,

$1\;{\text{nm}}={10^{ - 9}}\;{\text{m}}$

The wavelength and frequency of light are related to each other by the following expression,

${\text{c}} = {v\lambda}$                                   ......(1)

Here,

C is the speed of light.

$v$ is the frequency of light.

$\lambda$ is the wavelength of light.

Rearrange equation (1) to calculate the frequency of light.

$v=\dfrac{c}{\lambda}$                      ......(2)

The wavelength of yellow light is 580 nm.

Firstly, wavelength of yellow light is to be converted from nm to m as follows:

$\begin{aligned}{\text{Wavelength of yellow light }}\left({\text{m}}\right)&=\left( {{\text{580 nm}}}\right)\left({\frac{{{{10}^{ - 9}}\;{\text{m}}}}{{1\;{\text{nm}}}}}\right)\\&=58\times {10^{ - 10}}\;{\text{m}}\\\end{aligned}$

The speed of yellow light is $3 \times {10^8}\;{\text{m/s}}$.

The wavelength of yellow light is  $58\times {10^{ - 10}}\;{\text{m}}$.

Substitute these values in equation (2)

$\begin{aligned}{v }}&=\frac{{{\text{3}}\times{\text{1}}{{\text{0}}^8}\;{\text{m/s}}}}{{58 \times{{10}^{ - 10}}\;{\text{m}}}}\\&=0.05172\times{\text{1}}{{\text{0}}^{18}}\;{\text{Hz}}\\\end{aligned}$

So the frequency of yellow light is ${\mathbf{0}}{\mathbf{.05172 \times 1}}{{\mathbf{0}}^{{\mathbf{18}}}}\;{\mathbf{Hz}}$.

Learn more:

1. Statement about subatomic particle: brainly.com/question/3176193

2. The energy of a photon in light: brainly.com/question/7590814

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Structure of the atom

Keywords: frequency, wavelength, yellow light, 580 nm, crests, troughs, speed of light, wavelength of light, frequency of light, conversion factor, Hz, m.

Answer 2

Answer : The frequency of this yellow light is, $5.172\times 10^{14}s^{-1}$

Explanation : Given,

Wavelength of yellow light = $580nm=580\times 10^{-9}m$

conversion used : $1nm=1\times 10^{-9}m$

Formula used :

$\nu=\frac{c}{\lambda}$

where,

$\nu$ = frequency of light

$\lambda$ = wavelength of light

c = speed of light = $3\times 10^8m/s$

Now put all the given values in this formula, we get:

$\nu=\frac{3\times 10^8m/s}{580\times 10^{-9}m}=5.172\times 10^{14}s^{-1}$

Therefore, frequency of this yellow light is, $5.172\times 10^{14}s^{-1}$