How well can you know the momentum of the electron?

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SUMMARY

The discussion centers on the momentum of an electron in a hydrogen atom, specifically in its lowest energy state, where the radius is approximately 5x10^(-11) m. It is established that the momentum can be calculated using the formula p = h/λ, where h is Planck's constant (6.63 x 10^(-34) m^2 x kg/s). As energy is added to the electron, moving it to the fifth energy level, its momentum increases due to the higher energy state. The transitions between energy levels, particularly from level 5 to level 2 and from level 3 to level 2, result in the emission of photons in the visible spectrum, with the red photon corresponding to the transition from level 5 to level 2 and the blue photon corresponding to the transition from level 3 to level 2.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Planck's constant and its applications
  • Knowledge of energy levels in hydrogen atoms
  • Basic grasp of photon emission and wavelength concepts
NEXT STEPS
  • Study the concept of quantized angular momentum in quantum mechanics
  • Learn about the relationship between energy levels and photon emission in hydrogen
  • Explore the implications of the Heisenberg Uncertainty Principle on momentum and position
  • Investigate the mathematical derivation of the momentum formula p = h/λ
USEFUL FOR

Students and educators in physics, particularly those focusing on quantum mechanics, atomic structure, and photon interactions. This discussion is beneficial for anyone seeking to deepen their understanding of electron behavior in hydrogen atoms.

khorsani
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Consider the hydrogen atom (proton and electron)...
1. the radius of the lowest energy state is about 5x10^(-11) m. How
well can you know the momentum of the electron? In your solution, show
that you get units of momentum.

2. If energy is added, so that the electron moves up to the fifth
energy level, will the electron have moreor less momentum? Explain
your reasoning.

3. Consider two transitions:
(a) from level 5 to level 2
(b) from level 3 to level 2
both transitions produce photons in the visible range, one in the red
and the other in the blue. Which transition goes with which photon??
Justify your reasoning.
 
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CaptainZappo said:
Read the rules of the forum.

Ok, here what we know so far:

1. the electron has angular momentum.
2. But only certain values of angular momentum which are multiples of Plank's constant.
3. the combination of quantized energy and quantized angular momentum picks out only certain allowed orbits
4. so: the wavefronts are "quantized", only certain orbits are possible, only certain energies are possible, only certain angular momenta are possible and the light is emitted in transitions between orbits.
5. (The electron isn't following orbital paths in hydrogen, it is confined to regions of space)
6. Only two electrons end up in every energy-and-angular momentum combination

here I'm a little lost in understanding all this, but I'll keep trying

anyway:
p = h/lambda kg x m/s
p = 6.63 x 10^(-34) m^2 x kg/s

But I'm really lost at this point. Before answering can anyone refer me to a site where I could read more about it?

Thanks
 

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