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Calculate the frequency of each of the following wave lengths of electromagnetic radiation.

  • 632.8 nm (wavelength of red light from a helium-neon laser). Express your answer using three significant figures.
  • 503 nm (wavelength of maximum solar radiation). Express your answer using three significant figures.

This problem aims to familiarize us with the concepts of electromagnetic radiation along with its frequencies and wavelengths. This problem uses the basic understanding of classical physics, which involves electromagnetic waves, their interaction with matter, its characteristics, and the electromagnetic spectrum.

We can define electromagnetic radiation as a kind of energy revolving around us and taking numerous forms like radio waves, X-rays, microwaves, and lastly gamma-rays. If we look around us, we can discover that sunlight is also a type of electromagnetic energy, but visual light is only a tiny part of the electromagnetic spectrum. This electromagnetic spectrum contains a broad range of wavelengths.

Expert Answer

In this problem, we have been given the wavelength $(\lambda)$ of electromagnetic radiation and have been asked to compute the frequency $(v)$. Just a reminder that frequency and wavelength have an inverse relationship. This means that the wave with the highest frequency has the smallest wavelength. More precisely, twice the frequency indicates $ \dfrac{1}{2}$ the wavelength.

The formula that relates wavelength $(\lambda)$ with the frequency $(v)$ is given as:

\[c = \lambda v \]

Which can be rearranged as:

\[v=\dfrac{c}{\lambda} \]

Here, $c$ is the standard velocity that is $3 \times 10^8 \space m/s $.

And, $\lambda$ is the wavelength given $632.8 \times 10^{-9} \space m$.

Inserting the values:

\[ v = \dfrac{3 \times 10^8 \space m/s}{632.8 \times 10^{-9} \space m} \]

Frequency $(v)$ comes out to be:

\[v = 4.74 \times 10^{14} \space Hz\]

Part b:

The wavelength given in the question is $503 \times 10^{-9} \space m$.

Again, $c$ is the standard velocity that remains $3 \times 10^8 \space m/s $.

We have been asked to find the frequency $(v)$. The formula that relates wavelength $(\lambda)$ with the frequency $(v)$ is:

\[c = \lambda v\]

Rearranging it:

\[ v = \dfrac{c}{\lambda} \]

Now, inserting the values:

\[ v = \dfrac{3 \times 10^8 \space m/s}{503 \times 10^{-9} \space m} \]

Frequency $(v)$ comes out to be:

\[v = 5.96 \times 10^{14} \space Hz\]

Numerical Answer

Part a: Frequency of the electromagnetic radiation having wavelength $632.8 \space nm$ is $ 4.74 \times 10^{14} \space Hz $.

Part b: Frequency of the electromagnetic radiation having wavelength $503 \space nm$ is $ 5.96 \times 10^{14} \space Hz $.

Example

Calculate the frequency of the following wavelength of electromagnetic radiation.

  • $0.0520 \space nm$ (a wavelength used in medical X-rays) Express your answer using three significant figures.

The wavelength given in the question is $0.0520 \times 10^{-9} \space m $.

$c$ is the standard velocity that is $3 \times 10^8 \space m/s $.

We have been asked to find the frequency $(v)$. The formula is given as:

\[c=\lambda v\]

Rearranging it:

\[v=\dfrac{c}{\lambda}\]

Inserting the values:

\[v=\dfrac{3 \times 10^8 \space m/s}{0.052 \times 10^{-9} \space m}\]

Frequency $(v)$ comes out to be:

\[v=5.77 \times 10^{18} \space Hz\]

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