- 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:

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