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
![**Question:**
What is the wavelength in nm of a photon with a frequency of 92.2 MHz?
**Explanation:**
Frequency is given as 92.2 MHz (megahertz). To convert this to hertz, multiply by \(10^6\).
**Formula:**
The relationship between the speed of light \( (c) \), frequency \( (f) \), and wavelength \( (\lambda) \) is given by the formula:
\[
c = \lambda \cdot f
\]
Where:
- \( c \) is the speed of light (\(3 \times 10^8\) m/s)
- \( f \) is the frequency in Hz
- \( \lambda \) is the wavelength in meters
**Conversion:**
1. Convert frequency to Hz:
\[ 92.2 \text{ MHz} = 92.2 \times 10^6 \text{ Hz} \]
2. Rearrange the formula to solve for wavelength \( (\lambda) \):
\[ \lambda = \frac{c}{f} \]
3. Substitute the values into the formula to find the wavelength in meters, and then convert the result to nanometers (1 meter = \(10^9\) nanometers).
**Calculation Steps:**
1. Calculate wavelength in meters:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{92.2 \times 10^6 \text{ Hz}} \]
2. Convert the result to nanometers.
This calculation will yield the wavelength of the photon in nanometers, relating to the given frequency of 92.2 MHz.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7544060-01e3-4982-8714-99ffe5453575%2Fd5642b1f-a3a6-4692-8790-0cd212cd9f28%2F1xv68nk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the wavelength in nm of a photon with a frequency of 92.2 MHz?
**Explanation:**
Frequency is given as 92.2 MHz (megahertz). To convert this to hertz, multiply by \(10^6\).
**Formula:**
The relationship between the speed of light \( (c) \), frequency \( (f) \), and wavelength \( (\lambda) \) is given by the formula:
\[
c = \lambda \cdot f
\]
Where:
- \( c \) is the speed of light (\(3 \times 10^8\) m/s)
- \( f \) is the frequency in Hz
- \( \lambda \) is the wavelength in meters
**Conversion:**
1. Convert frequency to Hz:
\[ 92.2 \text{ MHz} = 92.2 \times 10^6 \text{ Hz} \]
2. Rearrange the formula to solve for wavelength \( (\lambda) \):
\[ \lambda = \frac{c}{f} \]
3. Substitute the values into the formula to find the wavelength in meters, and then convert the result to nanometers (1 meter = \(10^9\) nanometers).
**Calculation Steps:**
1. Calculate wavelength in meters:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{92.2 \times 10^6 \text{ Hz}} \]
2. Convert the result to nanometers.
This calculation will yield the wavelength of the photon in nanometers, relating to the given frequency of 92.2 MHz.
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