Final answer:
The momentum of a photon is inversely proportional to its wavelength. To calculate the electron's momentum after collision, one must consider the photon's change in momentum due to scattering, which requires the final wavelength post-collision. Without additional information, the electron's precise post-collision momentum cannot be determined.
Step-by-step explanation:
To find the magnitude of the linear momentum of an electron just after it collides with a photon, we use the principles of conservation of momentum and the relationship between photon momentum and its wavelength. The momentum p of a photon is given by the formula p = h/λ, where h is Planck's constant, and λ is the wavelength of the photon. Using Planck's constant 6.63×10−34 Js and the given initial wavelength 0.1010 nm, we can calculate the initial momentum of the photon. After the collision, the photon scatters at a certain angle, and its wavelength changes, implying a change in momentum. The electron, being initially at rest, gains momentum equal in magnitude and opposite in direction to the change in the photon's momentum. This is due to the law of conservation of momentum, which must be conserved in every direction.
However, to determine the exact magnitude of the electron's momentum after the collision, we would need to know the wavelength of the photon after the collision. This follows from the Compton effect, where the change in wavelength of the photon (Δλ) is related to the electron's momentum and the scattering angle. Without the final wavelength of the photon or additional details about the energy involved in the process, we cannot calculate the precise value of the electron's momentum post-collision.
It is important to note that a longer wavelength implies less momentum while a shorter wavelength implies more momentum. This is essential in understanding the relationship between photon wavelength and momentum, particularly in light of the Compton effect and the scattering processes of photons and electrons.