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For what wavelength of photon does compton scattering result in a photon whose energy is one half that of the original photon at a scattering angle of 45º? Give the answer as [a × 10–3 Å] . Find the value of a.
Correct answer is '7.085'. Can you explain this answer?
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For what wavelength of photon does compton scattering result in a phot...
The correct answer is: 7.085Most Upvoted Answer
For what wavelength of photon does compton scattering result in a phot...
Compton scattering is the scattering of a photon by an electron, resulting in a change in the wavelength and energy of the photon. The change in wavelength is given by the Compton wavelength shift equation:
Δλ = λ' - λ = h / (m_ec) * (1 - cosθ),
where Δλ is the change in wavelength, λ' is the final wavelength, λ is the initial wavelength, h is the Planck's constant, me is the electron mass, c is the speed of light, and θ is the scattering angle.
In this case, we are given that the scattering angle is 45 degrees, and we want to find the wavelength of the photon that results in half the energy of the original photon. The energy of a photon is given by the equation:
E = hc / λ,
where E is the energy, h is the Planck's constant, c is the speed of light, and λ is the wavelength.
Since we want the final photon to have half the energy of the original photon, we can write:
(E') / E = 1/2,
(hc) / (λ') / (hc) / λ = 1/2,
λ' / λ = 1/2.
Plugging this into the Compton wavelength shift equation and solving for λ:
Δλ = h / (m_ec) * (1 - cosθ),
λ' - λ = h / (m_ec) * (1 - cosθ),
λ / 2 - λ = h / (m_ec) * (1 - cos(45)),
-λ / 2 = h / (m_ec) * (1 - (√2)/2),
λ = -2 * (h / (m_ec)) * (1 - (√2)/2),
λ ≈ 1.242 × 10^(-12) meters.
Therefore, the wavelength of the resulting photon is approximately 1.242 × 10^(-12) meters.
Δλ = λ' - λ = h / (m_ec) * (1 - cosθ),
where Δλ is the change in wavelength, λ' is the final wavelength, λ is the initial wavelength, h is the Planck's constant, me is the electron mass, c is the speed of light, and θ is the scattering angle.
In this case, we are given that the scattering angle is 45 degrees, and we want to find the wavelength of the photon that results in half the energy of the original photon. The energy of a photon is given by the equation:
E = hc / λ,
where E is the energy, h is the Planck's constant, c is the speed of light, and λ is the wavelength.
Since we want the final photon to have half the energy of the original photon, we can write:
(E') / E = 1/2,
(hc) / (λ') / (hc) / λ = 1/2,
λ' / λ = 1/2.
Plugging this into the Compton wavelength shift equation and solving for λ:
Δλ = h / (m_ec) * (1 - cosθ),
λ' - λ = h / (m_ec) * (1 - cosθ),
λ / 2 - λ = h / (m_ec) * (1 - cos(45)),
-λ / 2 = h / (m_ec) * (1 - (√2)/2),
λ = -2 * (h / (m_ec)) * (1 - (√2)/2),
λ ≈ 1.242 × 10^(-12) meters.
Therefore, the wavelength of the resulting photon is approximately 1.242 × 10^(-12) meters.
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For what wavelength of photon does compton scattering result in a photon whose energy is one half that of the original photon at a scattering angle of 45º? Give the answer as [a× 10–3Å] . Find the value ofa.Correct answer is '7.085'. Can you explain this answer?
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For what wavelength of photon does compton scattering result in a photon whose energy is one half that of the original photon at a scattering angle of 45º? Give the answer as [a× 10–3Å] . Find the value ofa.Correct answer is '7.085'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For what wavelength of photon does compton scattering result in a photon whose energy is one half that of the original photon at a scattering angle of 45º? Give the answer as [a× 10–3Å] . Find the value ofa.Correct answer is '7.085'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what wavelength of photon does compton scattering result in a photon whose energy is one half that of the original photon at a scattering angle of 45º? Give the answer as [a× 10–3Å] . Find the value ofa.Correct answer is '7.085'. Can you explain this answer?.
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