Thank you for visiting Calculate the wavelength and energy of a photon with the following frequencies of electromagnetic radiation a 100 2 MHz FM radio b 1070 kHz AM. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Certainly! Let's solve the problem of finding the wavelength and energy of a photon with the given frequencies of electromagnetic radiation for both FM and AM radio.
### Step-by-Step Solution:
Constants Needed:
1. Speed of Light (c): Approximately [tex]\(3.00 \times 10^8\)[/tex] meters per second (m/s).
2. Planck's Constant (h): Approximately [tex]\(6.626 \times 10^{-34}\)[/tex] joules-seconds (J·s).
### Part a: FM Radio (Frequency = 100.2 MHz)
1. Convert Frequency to Hertz:
- The frequency of 100.2 MHz is equivalent to [tex]\(100.2 \times 10^6\)[/tex] Hz.
2. Calculate the Wavelength:
- Wavelength ([tex]\(\lambda\)[/tex]) is given by the formula:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Substituting the values:
- [tex]\(c = 3.00 \times 10^8\)[/tex] m/s
- [tex]\(f = 100.2 \times 10^6\)[/tex] Hz
- Calculate:
[tex]\[
\lambda \approx 2.994 \, \text{meters}
\][/tex]
3. Calculate the Energy of the Photon:
- Energy (E) is given by:
[tex]\[
E = h \times f
\][/tex]
- Substituting the values:
- [tex]\(h = 6.626 \times 10^{-34}\)[/tex] J·s
- [tex]\(f = 100.2 \times 10^6\)[/tex] Hz
- Calculate:
[tex]\[
E \approx 6.639252 \times 10^{-26} \, \text{joules}
\][/tex]
### Part b: AM Radio (Frequency = 1070 kHz)
1. Convert Frequency to Hertz:
- The frequency of 1070 kHz is equivalent to [tex]\(1070 \times 10^3\)[/tex] Hz.
2. Calculate the Wavelength:
- Using the same formula for wavelength:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Substituting the values:
- [tex]\(c = 3.00 \times 10^8\)[/tex] m/s
- [tex]\(f = 1070 \times 10^3\)[/tex] Hz
- Calculate:
[tex]\[
\lambda \approx 280.374 \, \text{meters}
\][/tex]
3. Calculate the Energy of the Photon:
- Using the formula for energy:
[tex]\[
E = h \times f
\][/tex]
- Substituting the values:
- [tex]\(h = 6.626 \times 10^{-34}\)[/tex] J·s
- [tex]\(f = 1070 \times 10^3\)[/tex] Hz
- Calculate:
[tex]\[
E \approx 7.08982 \times 10^{-28} \, \text{joules}
\][/tex]
This provides the wavelength and energy for both FM and AM radio frequencies.
### Step-by-Step Solution:
Constants Needed:
1. Speed of Light (c): Approximately [tex]\(3.00 \times 10^8\)[/tex] meters per second (m/s).
2. Planck's Constant (h): Approximately [tex]\(6.626 \times 10^{-34}\)[/tex] joules-seconds (J·s).
### Part a: FM Radio (Frequency = 100.2 MHz)
1. Convert Frequency to Hertz:
- The frequency of 100.2 MHz is equivalent to [tex]\(100.2 \times 10^6\)[/tex] Hz.
2. Calculate the Wavelength:
- Wavelength ([tex]\(\lambda\)[/tex]) is given by the formula:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Substituting the values:
- [tex]\(c = 3.00 \times 10^8\)[/tex] m/s
- [tex]\(f = 100.2 \times 10^6\)[/tex] Hz
- Calculate:
[tex]\[
\lambda \approx 2.994 \, \text{meters}
\][/tex]
3. Calculate the Energy of the Photon:
- Energy (E) is given by:
[tex]\[
E = h \times f
\][/tex]
- Substituting the values:
- [tex]\(h = 6.626 \times 10^{-34}\)[/tex] J·s
- [tex]\(f = 100.2 \times 10^6\)[/tex] Hz
- Calculate:
[tex]\[
E \approx 6.639252 \times 10^{-26} \, \text{joules}
\][/tex]
### Part b: AM Radio (Frequency = 1070 kHz)
1. Convert Frequency to Hertz:
- The frequency of 1070 kHz is equivalent to [tex]\(1070 \times 10^3\)[/tex] Hz.
2. Calculate the Wavelength:
- Using the same formula for wavelength:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Substituting the values:
- [tex]\(c = 3.00 \times 10^8\)[/tex] m/s
- [tex]\(f = 1070 \times 10^3\)[/tex] Hz
- Calculate:
[tex]\[
\lambda \approx 280.374 \, \text{meters}
\][/tex]
3. Calculate the Energy of the Photon:
- Using the formula for energy:
[tex]\[
E = h \times f
\][/tex]
- Substituting the values:
- [tex]\(h = 6.626 \times 10^{-34}\)[/tex] J·s
- [tex]\(f = 1070 \times 10^3\)[/tex] Hz
- Calculate:
[tex]\[
E \approx 7.08982 \times 10^{-28} \, \text{joules}
\][/tex]
This provides the wavelength and energy for both FM and AM radio frequencies.
Thank you for reading the article Calculate the wavelength and energy of a photon with the following frequencies of electromagnetic radiation a 100 2 MHz FM radio b 1070 kHz AM. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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