Scattering of Gamma Ray Photons

Gamma ray photons of energy 1.02 MeV are scattered from initially rest electrons. We are required to find the angle for symmetric scattering at this energy.

Understanding Scattering

Scattering is a phenomenon in which a particle or a wave is deflected or redirected due to interactions with other particles or objects. In the case of gamma ray photons scattering from electrons, the scattering occurs due to the electromagnetic interaction between the photon and the electron.

Scattering Angle

The angle for symmetric scattering refers to the angle at which the gamma ray photon is scattered with respect to its initial direction, such that the scattered photon travels at an equal angle on the opposite side of the incident direction. This angle is also known as the scattering angle of 180 degrees.

Compton Scattering

The scattering of gamma ray photons from electrons is known as Compton scattering. In Compton scattering, the incident photon transfers a portion of its energy and momentum to the electron, resulting in the deflection of the photon at a certain angle.

Compton Scattering Formula

The Compton scattering formula relates the change in wavelength (λ') of the scattered photon to the initial wavelength (λ) and the scattering angle (θ). It is given by:

λ' - λ = (h / m_e * c) * (1 - cosθ)

Where:
- λ' is the wavelength of the scattered photon
- λ is the initial wavelength of the 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

Calculating the Scattering Angle

To find the angle for symmetric scattering, we need to determine the scattering angle at which the change in wavelength is zero. In other words, we set λ' - λ = 0 in the Compton scattering formula and solve for θ.

0 = (h / m_e * c) * (1 - cosθ)

Simplifying the equation, we get:

cosθ = 1

Since cosθ = 1 at θ = 0, the symmetric scattering angle is 0 degrees.

However, it is important to note that in the context of this question, the correct answer is given as 41.4 degrees. This implies that there might be additional factors or conditions involved in determining the angle for symmetric scattering at this energy, which are not explicitly mentioned. Without further information or context, it is difficult to ascertain the exact reasoning behind the given answer.