Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
![**Problem Statement:**
A drone has a frequency of 3.91 GHz (gigahertz). What wavelength is associated with this frequency?
**Input:**
- Frequency: 3.91 GHz
**User Response:**
- Wavelength: 7.29 cm (This response is marked incorrect by a red "X" icon.)
**Concept Explanation:**
To find the wavelength associated with a given frequency, you can use the formula:
\[
\text{Wavelength} \ (\lambda) = \frac{c}{f}
\]
Where:
- \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) meters per second.
- \( f \) is the frequency.
To convert the frequency from gigahertz to hertz:
- \( 3.91 \ \text{GHz} = 3.91 \times 10^9 \ \text{Hz} \)
The calculated wavelength can be converted into centimeters by multiplying by 100 (1 meter = 100 cm).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F277ae00b-d056-42ed-a729-386f4fca5973%2F4303f27d-457d-4724-af18-deeca4fdccbc%2Fj3k2e3ho_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A drone has a frequency of 3.91 GHz (gigahertz). What wavelength is associated with this frequency?
**Input:**
- Frequency: 3.91 GHz
**User Response:**
- Wavelength: 7.29 cm (This response is marked incorrect by a red "X" icon.)
**Concept Explanation:**
To find the wavelength associated with a given frequency, you can use the formula:
\[
\text{Wavelength} \ (\lambda) = \frac{c}{f}
\]
Where:
- \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) meters per second.
- \( f \) is the frequency.
To convert the frequency from gigahertz to hertz:
- \( 3.91 \ \text{GHz} = 3.91 \times 10^9 \ \text{Hz} \)
The calculated wavelength can be converted into centimeters by multiplying by 100 (1 meter = 100 cm).
Transcribed Image Text:Remote control aerial vehicles (for example, drones) typically operate at gigahertz (GHz) frequencies, whereas cell phones operate using megahertz (MHz) frequencies. Calculate the wavelength associated with each of the following frequencies, if the speed of light is given as \(3.00 \times 10^8\) m/s.
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