College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question 29:** What is the frequency of red light whose wavelength is 700 nm?
**Explanation:**
To find the frequency (\(f\)) of red light with a wavelength (\(\lambda\)) of 700 nm, we use the formula that relates the speed of light (\(c\)), wavelength, and frequency:
\[ c = \lambda \times f \]
Where:
- \(c\) is the speed of light, approximately \(3 \times 10^8\) meters per second (m/s).
- \(\lambda\) is the wavelength in meters.
- \(f\) is the frequency in hertz (Hz).
**Steps:**
1. Convert the wavelength from nanometers to meters:
\[ 700 \text{ nm} = 700 \times 10^{-9} \text{ m} \]
2. Rearrange the formula to solve for frequency:
\[ f = \frac{c}{\lambda} \]
3. Substitute the values into the formula:
\[ f = \frac{3 \times 10^8 \text{ m/s}}{700 \times 10^{-9} \text{ m}} \]
4. Calculate the frequency:
\[ f \approx 4.29 \times 10^{14} \text{ Hz} \]
Thus, the frequency of red light with a wavelength of 700 nm is approximately \(4.29 \times 10^{14}\) Hz.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd32c0099-d35b-45af-b7af-24c06e9e82b9%2Ffa38e998-210a-4838-a6c0-61ffd55e47a4%2F5yhz3a_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 29:** What is the frequency of red light whose wavelength is 700 nm?
**Explanation:**
To find the frequency (\(f\)) of red light with a wavelength (\(\lambda\)) of 700 nm, we use the formula that relates the speed of light (\(c\)), wavelength, and frequency:
\[ c = \lambda \times f \]
Where:
- \(c\) is the speed of light, approximately \(3 \times 10^8\) meters per second (m/s).
- \(\lambda\) is the wavelength in meters.
- \(f\) is the frequency in hertz (Hz).
**Steps:**
1. Convert the wavelength from nanometers to meters:
\[ 700 \text{ nm} = 700 \times 10^{-9} \text{ m} \]
2. Rearrange the formula to solve for frequency:
\[ f = \frac{c}{\lambda} \]
3. Substitute the values into the formula:
\[ f = \frac{3 \times 10^8 \text{ m/s}}{700 \times 10^{-9} \text{ m}} \]
4. Calculate the frequency:
\[ f \approx 4.29 \times 10^{14} \text{ Hz} \]
Thus, the frequency of red light with a wavelength of 700 nm is approximately \(4.29 \times 10^{14}\) Hz.
Transcribed Image Text:This diagram illustrates the electromagnetic spectrum, showcasing the relationship between frequency (f) and wavelength (λ) of electromagnetic waves.
**Top Section: Frequency**
- The frequency (f) increases as you move from left to right, measured in hertz (Hz). Frequencies range from \(10^2\) Hz to \(10^{24}\) Hz.
**Bottom Section: Wavelength**
- The wavelength (λ) decreases as you move from left to right, measured in meters (m). Wavelengths range from \(10^6\) meters to \(10^{-14}\) meters.
**Sections of the Spectrum**
1. **Radio Waves**
- Characterized by low frequency and long wavelength.
- Includes AM and FM TV signals.
2. **Microwave**
- Used in radar technologies.
3. **Infrared**
4. **Visible Light**
- This section is magnified below, with wavelengths ranging approximately from 700 nm (red) to 400 nm (violet).
5. **Ultraviolet**
6. **X-rays**
7. **Gamma (γ) Waves**
- Characterized by high frequency and short wavelength.
Each section demonstrates the variety of electromagnetic waves, each with different applications and properties based on their respective frequencies and wavelengths. The visible light spectrum is highlighted with a color gradient, indicating the range of colors visible to the human eye from red to violet.
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