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Compton scattering occurs when a photon, which is a particle of light, collides with a free electron, causing the photon to scatter at a different angle and wavelength. The change in wavelength, known as the wavelength shift, is a key aspect of Compton scattering. It is calculated using the formula:
\[ \Delta \lambda = \frac{h}{m_e c} (1 - \cos \theta) \]
Here, \( h \) is Planck's constant, \( m_e \) is the mass of the electron, \( c \) is the speed of light, and \( \theta \) is the scattering angle.

• Planck's constant: \( 6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg/s} \)
• Electron mass: \( 9.109 \times 10^{-31} \, \text{kg} \)
• Speed of light: \( 3.00 \times 10^8 \, \text{m/s} \)

The wavelength shift, \( \Delta \lambda \), depends on the scattering angle \( \theta \). As the angle increases, the change in wavelength also becomes more significant.
Through calculations, the shift in this case is approximately \( 0.01499 \, \text{nm} \). This shift represents how far the photon's wavelength has moved from its original value due to the scattering process.

Photon energy is intrinsically linked to its wavelength. A photon's energy can be determined using the equation:

• \( E = \frac{hc}{\lambda} \)

Where \( E \) is the energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
In this problem, we calculate the photon energy before and after it experiences a wavelength shift due to scattering.

• Initial energy of the photon: Around \( 4.69 \times 10^{-15} \text{ J} \)
• Final energy after scattering: Around \( 3.47 \times 10^{-15} \text{ J} \)

This demonstrates that the photon loses energy as it changes wavelength. The negative energy change indicates this loss, reflecting the energy transfer to another particle鈥攊n this case, the electron.

When a photon undergoes Compton scattering, it's not just the photon that is affected鈥攖he scattering also impacts the electron it collides with. According to the conservation of energy, the total energy remains constant, meaning any energy lost by the photon must be gained by the electron.
In the presented situation, the photon loses \( 1.22 \times 10^{-15} \text{ J} \) of energy through scattering.
Hence, this energy is transferred to the electron, increasing its kinetic energy by the same amount.

• Energy gained by the electron: \( 1.22 \times 10^{-15} \text{ J} \)

This gain is crucial for understanding how photons and particles like electrons interact, showcasing a foundational principle of physics: energy conservation.
Each interaction between a photon and an electron, such as Compton scattering, provides insight into quantum mechanics and the dual nature of light. Understanding these processes is essential for fields like material science and medical imaging.