Energy/Frequency/Wavelength Worksheet Answer Key
Εγώ. Εισαγωγή
In this worksheet answer key, we will explore the concepts of energy, frequency, and wavelength and how they are related to each other. By understanding these concepts, we can better comprehend the behavior of waves and electromagnetic radiation in various fields of science.
II. Energy, Frequency, and Wavelength: Definitions
ΕΝΑ. Energy: Energy is the capacity to do work or produce heat. It is measured in joules (J) or electron volts (eV) in scientific contexts.
σι. Frequency: Frequency refers to the number of complete wave cycles that occur in one second. It is measured in hertz (Hz) or cycles per second.
ντο. Μήκος κύματος: Wavelength is the distance between two consecutive points of a wave that are in phase with each other. It is typically measured in meters (Μ), nanometers (nm), or angstroms (?).
III. Relationship between Energy, Frequency, and Wavelength
ΕΝΑ. The energy of a wave is directly proportional to its frequency: E ∝ ν. This means that higher frequency waves carry more energy.
σι. The energy of a wave is inversely proportional to its wavelength: E ∝ 1/λ. Consequently, shorter wavelength waves have higher energy.
ντο. The frequency and wavelength of a wave are inversely proportional to each other: ν ∝ 1/λ. As the frequency increases, the wavelength decreases, and vice versa.
IV. Problem Solving and Examples
To strengthen our understanding, let’s solve some problems and provide answers:
1. A wave has a frequency of 1000 Hz. What is its energy if the wave has a wavelength of 0.01 Μ?
Answer: Given: ν = 1000 Hz, λ = 0.01 Μ
Using E = hν, where h is the Planck’s constant (6.626 × 10^-34 J·s):
E = (6.626 × 10^-34 J·s) × (1000 Hz) = 6.626 × 10^-31 J
2. If the energy of a wave is 2.5 × 10^-18 eV and its frequency is 5.0 × 10^15 Hz, what is its wavelength in nanometers?
Answer: Given: E = 2.5 × 10^-18 eV, ν = 5.0 × 10^15 Hz
Converting eV to J: 1 eV = 1.602 × 10^-19 J
E = (2.5 × 10^-18 eV) × (1.602 × 10^-19 J/eV) = 4.005 × 10^-37 J
Using the equation E = hν and rearranging to λ = c/ν, where c is the speed of light (3.00 × 10^8 m/s):
λ = (3.00 × 10^8 m/s) / (5.0 × 10^15 Hz) = 6.0 × 10^-8 m = 60 nm
V. συμπέρασμα
Understanding the relationship between energy, frequency, and wavelength is crucial for comprehending the behavior of waves and electromagnetic radiation. This answer key has provided definitions, relationships, and solved examples to solidify the concepts. By mastering these concepts, scientists can unravel the mysteries of light, sound, and other wave phenomena in the world around us.
