Wavelength Of Red Light: Calculation Guide

Have you ever wondered how to calculate the wavelength of light, especially the vibrant red light emitted by neon signs? Guys, it's actually a fascinating journey into the world of physics, where we explore the relationship between frequency, wavelength, and the speed of light. In this guide, we'll break down the process step-by-step, making it super easy to understand. Let's dive in!

Understanding the Basics: Wavelength, Frequency, and the Speed of Light

Before we jump into the calculation, it's crucial to grasp the fundamental concepts. Wavelength, frequency, and the speed of light are interconnected, and understanding their relationship is key to solving this problem.

• Wavelength (λ): Imagine light as a wave. The wavelength is the distance between two consecutive crests or troughs of that wave. It's usually measured in meters (m) or nanometers (nm), where 1 nm equals 10^-9 meters. In simpler terms, think of it as the length of one complete wave cycle.

• Frequency (ν): Frequency refers to the number of wave cycles that pass a given point per unit of time. It's measured in Hertz (Hz), which represents cycles per second. So, a higher frequency means more waves are passing by each second, while a lower frequency means fewer waves.

• Speed of Light (c): This is a constant value, approximately 3.00 x 10^8 meters per second (m/s) in a vacuum. It represents how fast light travels through space. This constant is essential for our calculations.

The relationship between these three is beautifully captured in a simple equation:

c = λν

Where:

• c is the speed of light
• λ is the wavelength
• ν is the frequency

This equation tells us that the speed of light is equal to the product of the wavelength and the frequency. It's a cornerstone of physics and allows us to calculate one of these properties if we know the other two.

In our case, we're given the frequency of the red light and asked to find the wavelength. We already know the speed of light, so we have all the pieces we need to solve the puzzle!

Step-by-Step Calculation: Finding the Wavelength

Now, let's get to the exciting part: calculating the wavelength of the red light emitted by the neon sign. We'll follow a straightforward approach, using the equation we just discussed. Remember, our goal is to find the wavelength (λ) given the frequency (ν) and knowing the speed of light (c).

Here's how we'll do it:

1. Identify the Given Values: First, let's clearly state what we know. The problem tells us that the frequency (ν) of the red light is 4.84 x 10^14 Hz. We also know that the speed of light (c) is approximately 3.00 x 10^8 m/s.

2. Rearrange the Equation: Our equation is c = λν, but we want to find λ. So, we need to rearrange the equation to solve for wavelength. We can do this by dividing both sides of the equation by the frequency (ν):

   λ = c / ν

   This new equation tells us that the wavelength is equal to the speed of light divided by the frequency.

3. Plug in the Values: Now, we simply plug in the values we know into the rearranged equation:

   λ = (3.00 x 10^8 m/s) / (4.84 x 10^14 Hz)

4. Calculate the Wavelength in Meters: Performing the division, we get:

   λ ≈ 6.198 x 10^-7 meters

   This is the wavelength in meters, but the question asks for the wavelength in nanometers (nm). So, we need to convert meters to nanometers.

5. Convert Meters to Nanometers: Remember that 1 nm = 10^-9 m. To convert meters to nanometers, we multiply by the conversion factor 10^9:

   λ ≈ (6.198 x 10^-7 m) x (10^9 nm/m)

   λ ≈ 619.8 nm

6. Round to a Reasonable Number of Significant Figures: Depending on the level of precision required, we can round our answer. In this case, rounding to three significant figures is appropriate:

   λ ≈ 620 nm

So, the wavelength of the red light emitted by the neon sign is approximately 620 nm. That wasn't so hard, was it? By breaking down the problem into manageable steps and understanding the underlying physics, we were able to arrive at the solution.

Interpreting the Result: What Does 620 nm Mean?

Now that we've calculated the wavelength, let's take a moment to understand what our result, 620 nm, actually means. This number gives us valuable information about the nature of the red light emitted by the neon sign.

Wavelength is directly related to the color of light we perceive. The visible light spectrum, which is the portion of the electromagnetic spectrum that our eyes can see, ranges from approximately 400 nm to 700 nm. Different wavelengths within this range correspond to different colors.

• Shorter wavelengths (around 400 nm) correspond to violet and blue light.
• Longer wavelengths (around 700 nm) correspond to red light.
• Wavelengths in between represent the other colors of the rainbow: green, yellow, and orange.

Our calculated wavelength of 620 nm falls within the red portion of the visible spectrum. This makes perfect sense because the problem specifically mentions red light emitted by a neon sign. So, the calculation aligns with our expectations and reinforces our understanding of the relationship between wavelength and color.

Furthermore, the specific wavelength of light emitted by a neon sign is a characteristic property of the element neon. When neon atoms are excited (e.g., by an electrical discharge), they emit light at specific wavelengths. The strongest emission from neon is in the red part of the spectrum, which is why neon signs glow with their distinctive red color. Other elements emit light at different wavelengths, resulting in different colors in other types of signs.

Therefore, our calculation not only gives us a numerical value for the wavelength but also connects us to the fundamental physics of light emission and the unique properties of elements like neon.

Real-World Applications: Why This Calculation Matters

Understanding how to calculate the wavelength of light isn't just an academic exercise; it has numerous practical applications in various fields. This calculation is a fundamental tool in fields ranging from telecommunications to medicine.

• Telecommunications: Fiber optic cables use light to transmit data. The wavelength of the light used is crucial for determining the amount of data that can be transmitted and the distance it can travel. Engineers need to calculate and control the wavelength of light to ensure efficient data transmission.

• Spectroscopy: This technique analyzes the light emitted or absorbed by a substance to identify its components. By measuring the wavelengths of light, scientists can determine the chemical composition of materials, from stars in distant galaxies to samples in a laboratory.

• Medical Imaging: Techniques like MRI and PET scans use electromagnetic radiation, including light at different wavelengths, to create images of the inside of the body. Understanding wavelength is essential for developing and interpreting these images.

• Lighting and Displays: The wavelength of light emitted by LEDs and other light sources determines the color we see. This is crucial in designing everything from traffic lights to television screens.

• Astronomy: Astronomers use the wavelengths of light from stars and galaxies to determine their distance, speed, temperature, and composition. The Doppler effect, which shifts wavelengths due to motion, is a key tool in astronomical observations.

• Environmental Monitoring: Wavelengths of light are used in remote sensing to monitor environmental factors like air and water quality. Satellites equipped with sensors can detect specific wavelengths absorbed or reflected by pollutants.

The ability to calculate and manipulate wavelengths of light is fundamental to many technological advancements and scientific discoveries. It allows us to harness the power of light for communication, analysis, imaging, and countless other applications.

Conclusion: The Power of Understanding Light

Calculating the wavelength of light, like the red glow from a neon sign, might seem like a simple physics problem, but it opens the door to a deeper understanding of the world around us. We've seen how wavelength, frequency, and the speed of light are intertwined, and how this relationship allows us to determine the properties of light.

From the vibrant colors we see to the technologies that power our modern world, light plays a crucial role. By mastering the fundamentals of light calculations, we gain a powerful tool for exploring the universe and developing innovative solutions to real-world problems.

So, the next time you see a neon sign, remember the physics behind its glow. You now have the knowledge to calculate the wavelength of that light and appreciate the science that makes it possible. Keep exploring, keep learning, and keep shining a light on the wonders of physics!