Question

A certain kind of light has a wavelength of 850 nm. What is the frequency of this light in hz?.

Answer 1

So, the frequency of that light approximately $\sf{\bold{3.53 \times 10^{14} \: Hz}}$

Introduction

Hi ! I will help you to explain the relationship between velocity of electromagnetic waves in a vacuum with frequency and wavelength. We all know that all of the type of electromagnetic wave, will have the same velocity as the speed of light (because the value is a constant), which is 300,000 km/s or $\sf{3 \times 10^8}$ m/s. As a result of this constant property, the shorter the wavelength, the greater the value of the electromagnetic wave frequency. This relationship can also be expressed in this equation:

$\boxed{\sf{\bold{c = \lambda \times f}}}$

With the following condition :

• c = the constant of the speed of light in a vacuum ≈ $\sf{3 \times 10^{8} \: m/s}$ m/s
• $\sf{\lambda}$ = wavelength (m)
• f = electromagnetic wave frequency (Hz)

Problem Solving

We know that :

• c = the constant of the speed of light in a vacuum ≈ $\sf{3 \times 10^{8} \: m/s}$ m/s
• $\sf{\lambda}$ = wavelength = 850 nm = $\sf{8.5 \times 10^2 \times 10^{-9}}$ m = $\bold{8.5 \times 10^{-7} \: m}$

What was asked :

• f = electromagnetic wave frequency = ... Hz

Step by step :

$\sf{c = \lambda \times f}$

$\sf{3 \times 10^8 = 8.5 \times 10^{-7} \times f}$

$\sf{f = \frac{3 \times 10^8}{8.5 \times 10^{-7}}}$

$\sf{f \approx 0.353 \times 10^{8 -(-7)}}}$

$\sf{f \approx 3.53 \times 10^{-1} \times 10^{15}}$

$\boxed{\sf{f \approx 3.53 \times 10^{14} \: Hz}}$

Conclusion :

So, the frequency of that light approximately $\sf{\bold{3.53 \times 10^{14} \: Hz}}$

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