What is the wavelength in nm of a photon with a frequency of 92.2 MHz

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
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**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.
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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