Question

An electron of energy collides with a hydrogen atom in the ground state. The atom is excited to a higher energy state, and the electron is scattered with reduced velocity. The atom subsequently returns to its ground state with the emission of radiation of a wavelength. Find the velocity of the scattered electron.

Answer 1

The desired calculation of the scattered electron's velocity requires information on the energy of the collision, which isn't provided. In such interactions, conservation of energy and knowledge of the hydrogen atom's energy levels are usually applied.

Step-by-step explanation:

The student is asking about a scenario where an electron with a certain energy collides with a hydrogen atom, causing the atom to become excited and then return to its ground state by emitting radiation. The energy absorbed by the hydrogen atom raises an electron to a higher energy level, and when it falls back to the ground state, it emits a photon with a specific wavelength related to the energy difference between the two states.

Unfortunately, without the energy of the incoming electron, the initial energy state of the hydrogen atom, or the final energy state after collision, it is impossible to calculate the velocity of the scattered electron. To do so, we would typically apply conservation of energy principles and the known energy levels of a hydrogen atom, as we see in the example of the 21-centimeter line emission, which corresponds to a specific transition in hydrogen.