Wavelength and Frequency — Definition & Overview

What is Wavelength?

In terms of chemistry, wavelength has to do with light. Light travels in waves and wavelength measures the distance between waves. In the graph below the wavelength would be the distance between crests 1 and 2. Wavelength is typically measured by nanometers (nm) and described with lambda ($\lambda$).

What is Frequency?

It is the number of times a wave repeats in a sequence during a specific amount of time. Frequency is represented by nu ($\nu$) and measured in hertz or waves per second (Hz or $s^{-1}$). In the graph below the blue wave has a lower frequency and the green wave has a higher frequency.

Wavelength, Frequency, and Light

There are many types of light, which are described by the electromagnetic spectrum. Only some light is known as visible light and exists between 400-700nm. Typically as wavelength decreases, frequency increases.

The relationship between frequency and wavelength is described by this equation: $$c=\lambda\ \nu$$ The constant of light is represented by $c$ which has a value of 3.00 x 10$^8$ m/s. Note that when doing a calculation, nanometers should be converted to meters when calculating frequency.

Wavelength and Frequency

What Is Wavelength?

• Wavelength (λ) is defined as the distance between identical points on a wave for one wave cycle.

• Wavelength is typically measured using the distance between the crests/peaks of two adjacent waves.

• Wavelength is measured in units of length, usually nanometers (nm), meters (m), or sometimes centimeters (cm)

• The equation for wavelength is $λ=\frac{v}{f}$, where v is velocity, and f is frequency

• A larger wavelength corresponds to lower energy and a shorter wavelength corresponds to higher energy

What Is Frequency?

• Frequency (𝝂 or f) is defined as the number of waves that pass a given point for a given amount of time

• Frequency is measured in Hertz (Hz) or $s^{-1}$

• The equation for frequency is: $f=\frac{1}{T}$, where T is the period

• A higher frequency corresponds to higher energy and a lower frequency corresponds to lower energy

How Do Wavelength and Frequency Relate to Each Other?

• Wavelength and Frequency are inversely related to each other

• This means that a when there is a small wavelength, there will be a high frequency, and when there is a large wavelength there will be a low frequency

• This relationship can be visualized using the formula: c = λ𝝂, where c is the speed of light ($3.00x10^{8}$ m/s)

• Smaller wavelengths with higher frequency corresponds to light that is high in energy

• Larger wavelengths with lower frequencies correspond to light that is lower in energy

(Video) Frequency, Wavelength, and the Speed of Light

By Crash Chemistry Academy

This video looks at wavelength and energy in how they relate to light and the speed of light. The video answers important questions related to these topics.

1. What is frequency? It is represented by $\nu$ or nu and is the number of wave cycles per sec that pass through a single point.

2. What is the relationship between frequency ($\nu$) and wavelength ($\lambda$)? Wavelength is a measured distance of each wave. Two waves are shown which have different wavelength the top has a larger wavelength and the bottom has a smaller one. When moving the two waves at the same rate, the bottom wave passes through a given point more frequently that the top wave, which has a longer wavelength. This means that the bottom wave has a higher frequency and a shorter wavelength, the top wave has a shorter frequency and a longer wavelength.

3. How is frequency measured? The number of cycles per second is measured. The top wave is 0.86/s and the bottom is 2.1/s. It is also expressed as Hz or Hertz.

The speed of light is discussed at the distance light is able to travel and the amount of time that takes. Light travels at $3.00 \times 10^8 \frac{m}{s}$ represented by $c$ and it is a constant.

Light exists in a variety of wavelengths. A small range is called the visible spectrum, which humans are able to see with our eyes. The other ranges we cannot see, but are utilized. All of the light has the same speed, but differing wavelengths and frequencies.

Wavelength, frequency, and the speed of light are related to each other. This relationship is describes with the equation: $\lambda$$\nu$ = $c$. This means each wavelength has a frequency associated with it.

We've been studying the structure of atoms. We started with the discovery of the electron. JJ. Thompson's cathode ray experiment was the first contradiction of Dalton's atomic theory. Atoms had smaller subcomponents! As an explanation, Thompson proposed his plum pudding model. But, his model got dispelled by Rutherford's gold foil experiment. He found that atoms have a concentrated mass. In response, he proposed the nuclear model. It was a massive improvement from the plum pudding model. But it wasn't quite right.

In future lessons, we'll explore more atomic models. We'll start with Bohr's atomic model and then examine the quantum mechanical model. But to understand them, we need to take a quick detour. Both models require us to understand how electromagnetic radiation interacts with matter. So, we'll spend this lesson studying light!

Wavelength and Frequency in Chemistry

In classical physics, we considered electromagnetic radiation (light) to be a wave. Eventually, Albert Einstein solved the photoelectric effect by considering light as a particle. That would lead to the wave-particle duality. But in the late 1800s and early 1900s, we thought light was a wave. So, we have two ways to classify waves. We can use either their wavelength or their frequency.

The wavelength is a measure of length. So, it's the distance between identical points on consecutive cycles. I think it's easiest to measure from peak to peak or trough to trough. But if the locations are equivalent, the answer is always the same. You may have studied waves in math class. If you did, you most likely used radians. Please know that radians are not equivalent units to meters. Radians measure an angle. But in physics and chemistry, the wave travels linearly through space. So, the x-axis will be in meters.

The other option is frequency. Frequency is the number of cycles per second. We're seeing another way that physics and chemistry differ from math. If a wave is moving through space, there is a time component. The unit for frequency is Hertz (Hz). A Hertz is equivalent to a reciprocal second ($\frac{1}{s}$ or $s^{-1}$). Let's say we had a frequency of 400Hz. What does that tell us? The wave experiences four hundred cycles each second.

Relating Wavelength, Frequency, Momentum, and Energy

So, we can use either wavelength or frequency to describe light. But how do they relate? Let's consider the units. Wavelength is in meters. Frequency is in reciprocal seconds. What would happen if we multiplied them? We would have meters per second ($\frac{m}{s}$). That's the units for velocity. So, the equation is $v=\lambda\times\nu$. $\lambda$ is the symbol for wavelength. $\nu$ is the symbol for frequency. This equation works for any wave. But, we're discussing light. So, we can alter it to $c=\lambda\times\nu$. $c$ is the notation for the speed of light in a vacuum. It's equal to $299792458\frac{m}{s}$. Please note this is a specific value for light in a vacuum. If the light is traveling through another material, the value changes.

Since light has a wavelength and a frequency, we can calculate its energy and momentum. We'll learn more when we begin studying quantum mechanics. But for now, here are the equations. The energy equation is $E=h\nu$. $h$ is Planck's constant ($6.626\times10^{-34}$ Joule-sec). We'll learn about it when we study Planck's quantum theory. The momentum equation is $p=h\times\nu\times c$.

Atomic Spectra

So, how does all of this relate to chemistry? In a future lesson, we'll study atomic spectra. But for now, know that an atom's electrons can absorb and emit light. When light hits an electron, the electron gets elevated to a higher energy level. But there's a catch! Only specific wavelengths or frequencies work. That's because electrons can only absorb exact energies. If there is too little energy, nothing happens. We say that the energy is quantized.

So, once an electron gets promoted, how does it lose that energy? It has to emit light. When an electron falls to a lower energy level, it releases a photon. The light's energy equals the difference between the energy levels. Again, the energy has a specific quantity. Why? Because energy levels are quantized.

It turns out that chemists can measure an atom's absorbed and emitted frequencies. What's the result? A spectrum of frequencies. We know that many chemists were developing various atomic models. A successful model would theoretically predict the spectra. In future lessons, we'll see that the Bohr model predicted the hydrogen and helium ion spectra. But, it failed for larger elements. The quantum mechanical model proved more accurate for heavier elements.

Using Light: Analytical Chemistry

Why do we spend so much time learning about light? For analytical chemists, light has a variety of applications. Spectroscopy is an analytical tool that studies the interaction between matter and electromagnetic radiation. What does that mean practically? In spectroscopy, we shine light through a sample. How light interacts with the sample's atoms and molecules tells us valuable information. But there's a catch! Different wavelengths of light have unique interactions.

Let's look at a few different types of spectroscopy. In IR spectroscopy, we use infrared light. It turns out that IR radiation causes covalent bonds to stretch and bend. But these occur at distinct wavelengths for various bonds. For example, let's consider a carbon-oxygen bond. A single bond will have a different wavelength than a double bond. The chemist can tell what types of bonds are present from the absorbed wavelengths.

What's another example? Let's say we had a solution with an unknown concentration. We could use UV-visible spectroscopy. The sample's molarity is related to absorption by the Beer-Lambert law. For example, in college, I performed an experiment using UV-visible spectroscopy. Our goal was to find the amount of iron in a sample. First, you have to make a calibration curve. To do that, you make solutions with various concentrations and measure the absorbance. You've created a calibration curve. Then, you measure your unknown sample's absorbance. From the calibration curve, you can determine the concentration!

Let's consider one last example. X-ray crystallography uses x-rays to determine three-dimensional crystal structures. Remember, in crystals, the atoms arrange to form a lattice. X-rays have a lot of energy. So they diffract off the atoms' electrons. The angle of diffraction allows the chemist to specify the atoms' locations. The most famous example of using X-ray crystallography was the discovery of DNA's double-helix structure. So, you can see that X-ray crystallography is a powerful technique.

So what's the overall takeaway? In general chemistry, you don't need to worry about the different types of spectroscopy. But, you do need to understand the interaction of light and matter. Different wavelengths of light interact with atoms and molecules in unique ways. That's why we spend so much time studying light.