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A beam of X-Ray of wavelength 0.2 nm is incident on a free electron and gets scattered in a direction with respect to the direction of the incident radiation resulting in maximum wavelength shift. Then find out percentage energy loss of the incident radiation.
Correct answer is '2.4'. Can you explain this answer?
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A beam of X-Ray of wavelength 0.2 nm is incident on a free electron an...
Compton shift 
For maximum shift
Energy of radiation
log E = log hc - logλ
taking derivative
Percentage energy loss
For maximum shift
Energy of radiation
log E = log hc - logλ
taking derivative
Percentage energy loss
Most Upvoted Answer
A beam of X-Ray of wavelength 0.2 nm is incident on a free electron an...
Scattering of X-Rays by Free Electrons
When X-rays interact with matter, they can undergo scattering, which involves a change in direction and energy. In this case, the incident X-ray beam with a wavelength of 0.2 nm is scattered by a free electron, resulting in a maximum wavelength shift. We need to determine the percentage energy loss of the incident radiation.
Compton Scattering
The scattering of X-rays by free electrons is known as Compton scattering. This phenomenon occurs when an X-ray photon interacts with an electron, transferring some of its energy and changing its direction. The scattered photon has a longer wavelength compared to the incident photon.
Wavelength Shift and Energy Loss
The maximum wavelength shift in Compton scattering occurs when the scattered photon is scattered at an angle of 180 degrees with respect to the incident photon. In this case, the change in wavelength, Δλ, can be calculated using the Compton wavelength shift formula:
Δλ = λ' - λ = h / (m_e * c) * (1 - cosθ)
Where:
- Δλ is the change in wavelength
- λ' is the wavelength of the scattered photon
- λ is the wavelength of the incident photon
- h is the Planck's constant
- m_e is the mass of the electron
- c is the speed of light
- θ is the scattering angle
The energy of a photon is inversely proportional to its wavelength, so the energy loss of the incident radiation can be calculated as a percentage using the formula:
Energy loss (%) = (Δλ / λ) * 100
Calculating the Wavelength Shift
In this case, the maximum wavelength shift occurs when the scattering angle, θ, is 180 degrees. Plugging this value into the Compton wavelength shift formula, we can calculate the change in wavelength:
Δλ = h / (m_e * c) * (1 - cos180°)
= 2h / (m_e * c)
Calculating the Energy Loss
To calculate the percentage energy loss, we need to divide the change in wavelength by the incident wavelength and multiply by 100:
Energy loss (%) = (Δλ / λ) * 100
= (2h / (m_e * c)) / λ * 100
Substituting the given values:
Energy loss (%) = (2 * 6.626 x 10^(-34) J s) / ((9.11 x 10^(-31) kg) * (3 x 10^8 m/s)) / (0.2 x 10^(-9) m) * 100
≈ 2.4%
Therefore, the percentage energy loss of the incident radiation is approximately 2.4%.
When X-rays interact with matter, they can undergo scattering, which involves a change in direction and energy. In this case, the incident X-ray beam with a wavelength of 0.2 nm is scattered by a free electron, resulting in a maximum wavelength shift. We need to determine the percentage energy loss of the incident radiation.
Compton Scattering
The scattering of X-rays by free electrons is known as Compton scattering. This phenomenon occurs when an X-ray photon interacts with an electron, transferring some of its energy and changing its direction. The scattered photon has a longer wavelength compared to the incident photon.
Wavelength Shift and Energy Loss
The maximum wavelength shift in Compton scattering occurs when the scattered photon is scattered at an angle of 180 degrees with respect to the incident photon. In this case, the change in wavelength, Δλ, can be calculated using the Compton wavelength shift formula:
Δλ = λ' - λ = h / (m_e * c) * (1 - cosθ)
Where:
- Δλ is the change in wavelength
- λ' is the wavelength of the scattered photon
- λ is the wavelength of the incident photon
- h is the Planck's constant
- m_e is the mass of the electron
- c is the speed of light
- θ is the scattering angle
The energy of a photon is inversely proportional to its wavelength, so the energy loss of the incident radiation can be calculated as a percentage using the formula:
Energy loss (%) = (Δλ / λ) * 100
Calculating the Wavelength Shift
In this case, the maximum wavelength shift occurs when the scattering angle, θ, is 180 degrees. Plugging this value into the Compton wavelength shift formula, we can calculate the change in wavelength:
Δλ = h / (m_e * c) * (1 - cos180°)
= 2h / (m_e * c)
Calculating the Energy Loss
To calculate the percentage energy loss, we need to divide the change in wavelength by the incident wavelength and multiply by 100:
Energy loss (%) = (Δλ / λ) * 100
= (2h / (m_e * c)) / λ * 100
Substituting the given values:
Energy loss (%) = (2 * 6.626 x 10^(-34) J s) / ((9.11 x 10^(-31) kg) * (3 x 10^8 m/s)) / (0.2 x 10^(-9) m) * 100
≈ 2.4%
Therefore, the percentage energy loss of the incident radiation is approximately 2.4%.
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A beam of X-Ray of wavelength 0.2 nm is incident on a free electron and gets scattered in a direction with respect to the direction of the incident radiation resulting in maximum wavelength shift. Then find out percentage energy loss of the incident radiation.Correct answer is '2.4'. Can you explain this answer?
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