Collision of a free electron and a hydrogen atom - energies

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Homework Help Overview

The discussion revolves around the collision of a free electron with a hydrogen atom in its ground state, specifically focusing on the kinetic energy (KE) of the electron and the potential outcomes of the collision. The original poster presents a scenario where the electron has a known kinetic energy of 11.5 eV and explores the possible kinetic energy after the collision.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster considers two scenarios: the electron colliding with an orbiting electron, leading to excitation, or missing it, resulting in unchanged kinetic energy. They question the conditions under which the orbiting electron would absorb maximum energy and the implications of the term 'rebounding' when the electron does not collide with the orbiting electron. Other participants discuss the nature of collisions with the nucleus and the quantized energy states of the orbiting electron, raising questions about energy transitions and the feasibility of exciting the electron to different energy levels.

Discussion Status

The discussion is active, with participants exploring various interpretations of the collision dynamics and energy transfer. Some guidance has been offered regarding the quantized states of the orbiting electron and the implications of the collision with the nucleus, but there is no explicit consensus on the nature of the rebound or the energy levels involved.

Contextual Notes

Participants are navigating the complexities of energy transitions in quantum mechanics, including the constraints of quantized energy levels and the assumptions about energy transfer during collisions. The original poster expresses uncertainty about the correctness of their interpretations and the underlying principles.

kapitan90
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Homework Statement


An electron of know KE collides with a hydrogen atom in its ground state. With what possible KE may it rebound?
KE = 11.5 eV

2. The attempt at a solution
I assumed that the electron may either hit an orbiting electron and excite him (maximum layer is n = 2, change in KE = 11.5 - (13.6 - 3.4) = 1.3 eV)
or miss it (KE unaltered = 11.5eV)

Those answers are correct, yet I don't understand them fully.

3. Relevant questions
How do we know that the orbiting electron will take the maximum amount of energy it can take? Is it a simplification or a free electron has to give this amount of energy to the orbiting electron? Why?

Also, can we speak of 'rebounding off the atom' if the electron doesn't hit the free electron? It cannot collide with atom's nucleus as it's energy is unaltered, so how may it rebound?
 
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If it collides with the nucleus, since the nucleus is so massive, it will just bounce right back with its energy unchanged. It is like throwing a ball against a brick wall.

The orbiting electron can only exist in quantized states. To see why, you will have to solve the Schrödinger equation. The energy of any state is

E_n = - \frac{E_0}{n^2}

where n is an integer, and E0 is the ground state energy 13.6eV. So the incident electron can only rebound with quantized energy levels.

K_f = K_i - \Delta E_{atom} = K_i - (E_n - E_0)
 
But why can't an orbiting electron be excited to n = 1, only to n = 2?
 
kapitan90 said:
But why can't an orbiting electron be excited to n = 1, only to n = 2?

For higher transitions, it will take more and more energy. Does the incident electron have enough energy to make the orbiting electron transfer from n=1 to n=3?
 

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