An electron scatters incoming x rays of 110 pm at an angle of 40°. Find the energy of the scattered photon.
An electron scatters incoming x rays of 110 pm at an angle of 40°. Find the energy of the scattered photon.
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![## Problem Statement:
**Physics: Compton Scattering**
An electron scatters incoming x-rays of 110 pm at an angle of 40°. Find the energy of the scattered photon.
### Explanation:
In this problem, x-rays with a wavelength of 110 pm (picometers) are scattered at an angle of 40° by an electron. The objective is to find the energy of the scattered photon.
To solve this, you will need to apply the Compton Scattering formula and convert the resultant wavelength into energy.
### Compton Scattering Formula:
\[ \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos\theta) \]
Where:
- \(\lambda'\) is the wavelength of the scattered photon.
- \(\lambda\) is the initial wavelength of the photon.
- \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) J·s).
- \(m_e\) is the electron mass (\(9.109 \times 10^{-31}\) kg).
- \(c\) is the speed of light (\(3 \times 10^8\) m/s).
- \(\theta\) is the scattering angle (40° in this case).
To find the energy of the scattered photon, you can use the energy-wavelength relation:
\[ E' = \frac{hc}{\lambda'} \]
Here, \(E'\) represents the energy of the scattered photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda'\) is the wavelength of the scattered photon.
### Steps to Solve:
1. Calculate the change in wavelength (\(\Delta \lambda\)).
2. Determine the new wavelength (\(\lambda'\)).
3. Calculate the energy of the scattered photon using the new wavelength.
By following these steps and inserting the given parameters, you will be able to determine the energy of the scattered photon.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F56979f35-7982-4683-b3f7-d18cf55191f9%2Fq77crsq_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement:
**Physics: Compton Scattering**
An electron scatters incoming x-rays of 110 pm at an angle of 40°. Find the energy of the scattered photon.
### Explanation:
In this problem, x-rays with a wavelength of 110 pm (picometers) are scattered at an angle of 40° by an electron. The objective is to find the energy of the scattered photon.
To solve this, you will need to apply the Compton Scattering formula and convert the resultant wavelength into energy.
### Compton Scattering Formula:
\[ \lambda' - \lambda = \frac{h}{m_e c} (1 - \cos\theta) \]
Where:
- \(\lambda'\) is the wavelength of the scattered photon.
- \(\lambda\) is the initial wavelength of the photon.
- \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) J·s).
- \(m_e\) is the electron mass (\(9.109 \times 10^{-31}\) kg).
- \(c\) is the speed of light (\(3 \times 10^8\) m/s).
- \(\theta\) is the scattering angle (40° in this case).
To find the energy of the scattered photon, you can use the energy-wavelength relation:
\[ E' = \frac{hc}{\lambda'} \]
Here, \(E'\) represents the energy of the scattered photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda'\) is the wavelength of the scattered photon.
### Steps to Solve:
1. Calculate the change in wavelength (\(\Delta \lambda\)).
2. Determine the new wavelength (\(\lambda'\)).
3. Calculate the energy of the scattered photon using the new wavelength.
By following these steps and inserting the given parameters, you will be able to determine the energy of the scattered photon.
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