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
![### Question:
An EM wave has a frequency of \(2 \times 10^{14}\) Hz. What is the wavelength?
### Options:
- A. 1.5 nm
- B. 1.5 km
- C. 1.5 µm
- D. 1.5 mm
- E. 1.5 cm
### Explanation:
This question requires calculating the wavelength of an electromagnetic (EM) wave given its frequency. To solve, use the wave equation:
\[ c = \lambda \times f \]
where:
- \( c \) is the speed of light (\(3 \times 10^8\) m/s),
- \( \lambda \) is the wavelength,
- \( f \) is the frequency.
### Step-by-Step Solution:
1. Rearrange the equation to solve for wavelength:
\[ \lambda = \frac{c}{f} \]
2. Substitute the given values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{2 \times 10^{14} \text{ Hz}} \]
3. Calculate the wavelength:
\[ \lambda = 1.5 \times 10^{-6} \text{ m} \]
4. Convert meters to micrometers (\(1 \text{ m} = 10^6 \text{ µm}\)):
\[ \lambda = 1.5 \text{ µm} \]
### Answer:
The correct answer is C. 1.5 µm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ac3fb34-d67d-45d3-9547-9a9b3f582708%2Fba5c5289-73b5-496e-b73e-7bcc8f5eb8a9%2F65lqld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question:
An EM wave has a frequency of \(2 \times 10^{14}\) Hz. What is the wavelength?
### Options:
- A. 1.5 nm
- B. 1.5 km
- C. 1.5 µm
- D. 1.5 mm
- E. 1.5 cm
### Explanation:
This question requires calculating the wavelength of an electromagnetic (EM) wave given its frequency. To solve, use the wave equation:
\[ c = \lambda \times f \]
where:
- \( c \) is the speed of light (\(3 \times 10^8\) m/s),
- \( \lambda \) is the wavelength,
- \( f \) is the frequency.
### Step-by-Step Solution:
1. Rearrange the equation to solve for wavelength:
\[ \lambda = \frac{c}{f} \]
2. Substitute the given values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{2 \times 10^{14} \text{ Hz}} \]
3. Calculate the wavelength:
\[ \lambda = 1.5 \times 10^{-6} \text{ m} \]
4. Convert meters to micrometers (\(1 \text{ m} = 10^6 \text{ µm}\)):
\[ \lambda = 1.5 \text{ µm} \]
### Answer:
The correct answer is C. 1.5 µm.
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