Calculate the frequency of a 4 MeV photon.
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![**Problem: Calculate the Frequency of a Photon**
**Given:**
Energy of the photon (E) = 4 MeV
A photon's energy (E) can be related to its frequency (f) via the Planck-Einstein relation:
\[ E = h \cdot f \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\[ h \approx 6.626 \times 10^{-34} \text{ Js} \]),
- \( f \) is the frequency of the photon.
First, convert the given energy from mega-electronvolts (MeV) to joules (J), knowing that:
\[ 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \]
\[ 1 \text{ MeV} = 10^6 \text{ eV} \]
Thus,
\[ E = 4 \text{ MeV} = 4 \times 10^6 \text{ eV} \]
\[ E = 4 \times 10^6 \times 1.602 \times 10^{-19} \text{ J} \]
\[ E = 6.408 \times 10^{-13} \text{ J} \]
Now solve for the frequency (\( f \)):
\[ f = \frac{E}{h} \]
Substitute the values:
\[ f = \frac{6.408 \times 10^{-13}}{6.626 \times 10^{-34}} \]
\[ f ≈ 9.67 \times 10^{20} \text{ Hz} \]
Therefore, the frequency of a 4 MeV photon is approximately \( 9.67 \times 10^{20} \text{ Hz} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fdfc26a-e6d8-4dfd-b2bf-654dccb4509d%2F68b663d9-9641-44d5-8df0-2e385e62a029%2Fq65tl9h_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Calculate the Frequency of a Photon**
**Given:**
Energy of the photon (E) = 4 MeV
A photon's energy (E) can be related to its frequency (f) via the Planck-Einstein relation:
\[ E = h \cdot f \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\[ h \approx 6.626 \times 10^{-34} \text{ Js} \]),
- \( f \) is the frequency of the photon.
First, convert the given energy from mega-electronvolts (MeV) to joules (J), knowing that:
\[ 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \]
\[ 1 \text{ MeV} = 10^6 \text{ eV} \]
Thus,
\[ E = 4 \text{ MeV} = 4 \times 10^6 \text{ eV} \]
\[ E = 4 \times 10^6 \times 1.602 \times 10^{-19} \text{ J} \]
\[ E = 6.408 \times 10^{-13} \text{ J} \]
Now solve for the frequency (\( f \)):
\[ f = \frac{E}{h} \]
Substitute the values:
\[ f = \frac{6.408 \times 10^{-13}}{6.626 \times 10^{-34}} \]
\[ f ≈ 9.67 \times 10^{20} \text{ Hz} \]
Therefore, the frequency of a 4 MeV photon is approximately \( 9.67 \times 10^{20} \text{ Hz} \).
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