Energy, Frequency, & Wavelength Worksheet Answer Key
Table of Contents :
Energy, frequency, and wavelength are fundamental concepts in the field of physics, particularly when it comes to understanding electromagnetic waves. The relationship among these three variables is essential for various scientific applications, from telecommunications to understanding the behavior of light. In this blog post, we will explore these concepts in detail, providing examples and a worksheet answer key to facilitate learning.
Understanding Energy, Frequency, and Wavelength
What is Energy? ⚡
Energy is the capacity to do work or produce heat. It exists in various forms, including kinetic, potential, thermal, and electromagnetic energy. In the context of electromagnetic waves, energy is related to the frequency of the wave. Higher frequency waves carry more energy, while lower frequency waves carry less.
What is Frequency? 🎶
Frequency refers to the number of cycles of a wave that pass a point in one second, measured in Hertz (Hz). In the electromagnetic spectrum, frequencies can vary from extremely low (like radio waves) to extremely high (like gamma rays). The frequency of a wave is inversely proportional to its wavelength; as frequency increases, wavelength decreases.
What is Wavelength? 🌊
Wavelength is the distance between consecutive crests (or troughs) of a wave, typically measured in meters (m). It is a crucial factor in determining the type of electromagnetic wave, as different wavelengths correspond to different regions of the electromagnetic spectrum.
The Relationship Between Energy, Frequency, and Wavelength
The relationship among energy (E), frequency (f), and wavelength (λ) can be described by the following formulas:
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Energy and Frequency: [ E = h \cdot f ] where (h) is Planck's constant ((6.626 \times 10^{-34} , \text{Js})).
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Frequency and Wavelength: [ c = f \cdot \lambda ] where (c) is the speed of light in a vacuum ((3.00 \times 10^8 , \text{m/s})).
From these equations, we can derive that:
[ E = \frac{h \cdot c}{\lambda} ]
This equation shows how energy is inversely proportional to wavelength: as the wavelength increases, the energy decreases.
Practical Applications 📊
Understanding the relationship between energy, frequency, and wavelength is vital in several fields, including:
- Telecommunications: Different frequencies are used for different types of communication (radio, television, cell phones).
- Medicine: X-rays have higher energy and shorter wavelengths, making them useful for imaging but also requiring careful handling.
- Astronomy: Observing different wavelengths of light helps scientists understand distant celestial objects.
Worksheet Example 📋
To reinforce the understanding of energy, frequency, and wavelength, here’s a sample worksheet with a variety of problems. Below is a simplified version of how this worksheet could look:
<table> <tr> <th>Problem</th> <th>Formula</th> <th>Answer</th> </tr> <tr> <td>1. Calculate the energy of a photon with a frequency of 5 x 10<sup>14</sup> Hz.</td> <td>E = h * f</td> <td>3.31 x 10<sup>-19</sup> J</td> </tr> <tr> <td>2. What is the wavelength of a wave with a frequency of 2.5 x 10<sup>14</sup> Hz?</td> <td>c = f * λ</td> <td>1.2 x 10<sup>-6</sup> m</td> </tr> <tr> <td>3. Find the frequency of a photon with an energy of 2.5 x 10<sup>-19</sup> J.</td> <td>E = h * f</td> <td>3.77 x 10<sup>14</sup> Hz</td> </tr> <tr> <td>4. Calculate the wavelength of a wave with an energy of 1.24 x 10<sup>-18</sup> J.</td> <td>E = (h * c) / λ</td> <td>1.6 x 10<sup>-10</sup> m</td> </tr> </table>
Answer Key 🗝️
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Energy of a photon with a frequency of 5 x 10<sup>14</sup> Hz:
- E = h * f
- E = (6.626 \times 10^{-34} , \text{Js} \cdot 5 \times 10^{14} , \text{Hz})
- E = 3.31 x 10<sup>-19</sup> J
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Wavelength of a wave with a frequency of 2.5 x 10<sup>14</sup> Hz:
- c = f * λ
- λ = (c / f = (3.00 \times 10^8 , \text{m/s}) / (2.5 \times 10^{14} , \text{Hz}))
- λ = 1.2 x 10<sup>-6</sup> m
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Frequency of a photon with an energy of 2.5 x 10<sup>-19</sup> J:
- E = h * f
- f = E / h = (2.5 \times 10^{-19} , \text{J} / 6.626 \times 10^{-34} , \text{Js})
- f = 3.77 x 10<sup>14</sup> Hz
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Wavelength of a wave with an energy of 1.24 x 10<sup>-18</sup> J:
- E = (h * c) / λ
- λ = (h * c) / E = ((6.626 \times 10^{-34} , \text{Js} \cdot 3.00 \times 10^8 , \text{m/s}) / (1.24 \times 10^{-18} , \text{J}))
- λ = 1.6 x 10<sup>-10</sup> m
Important Notes 📌
- "Understanding these concepts is not just about memorization but also about grasping their relationships."
- "Make sure to practice with different problems to solidify your understanding."
By thoroughly understanding energy, frequency, and wavelength, students and enthusiasts alike can apply this knowledge to numerous scientific and practical fields, enhancing their learning and comprehension of physics.