Respuesta :

The frequency of yellow light of wavelength 580 nm is  [tex]\boxed{{0.05172\times10^{18}}\text{Hz}}[/tex]

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 [tex]\lambda[/tex] 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 [tex]{\text{v }}[/tex] and its SI unit is Hertz (Hz).

The conversion factor to convert nm to m is,

[tex]1\;{\text{nm}}={10^{ - 9}}\;{\text{m}}[/tex]

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

[tex]{\text{c}} = {v\lambda}[/tex]                                   ......(1)

Here,

C is the speed of light.

[tex]v[/tex] is the frequency of light.

[tex]\lambda[/tex] is the wavelength of light.

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

[tex]v=\dfrac{c}{\lambda}[/tex]                      ......(2)

The wavelength of yellow light is 580 nm.

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

[tex]\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}[/tex]

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

The wavelength of yellow light is  [tex]58\times {10^{ - 10}}\;{\text{m}}[/tex].

Substitute these values in equation (2)

[tex]\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}[/tex]

So the frequency of yellow light is [tex]{\mathbf{0}}{\mathbf{.05172 \times 1}}{{\mathbf{0}}^{{\mathbf{18}}}}\;{\mathbf{Hz}}[/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: frequency, wavelength, yellow light, 580 nm, crests, troughs, speed of light, wavelength of light, frequency of light, conversion factor, Hz, m.

adioabiola

The frequency of this yellow light with wavelength, 580.0 nm is; 5.2 × 10¹⁴ Hz.

According to the question:

  • The wavelength of the yellow light is 580.0 nm.

  • By convention, the speed of light (photons), c = 3×10⁸ m/s.

We must also establish the relationship between the speed, wavelength and frequency as follows;

c = f × λ

Therefore, f = c/λ

where,

  • c = speed of light
  • f = frequency
  • λ = wavelength.

However, 580nm = 580 × 10^-⁹ m = 5.8 × 10-⁷m

  • Since, 1nm = 10^-9m

Consequently, the frequency, f of this yellow light is;

  • f = 3×10⁸/5.8 × 10^-⁷

  • f = 5.2 × 10¹⁴ Hz.

Read more:

https://brainly.com/question/25009190

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