How Does Electron Momentum Change Across Hydrogen Atom Energy Levels?

[khorsani]

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.

P=mv

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.

So does this make any sense, am I on the right path?


f= c/lambda

E upper - E lower = hf

thus it follows that:

1/hc(E upper - E lower) = 1/lambda = R (1/2squared - 1/n squared)

and then I need Balmers formula to find the energy level in terms of the kinetic and potential energy? Am I on the right path?


Here is a response from 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

 

[Dick]

The first one is an uncertainty principle problem. Neither of the other two require an exact calculation. For the second one, just apply the same logic as in the first one. For the third you just need to know whether the energy difference between 5 and 2 is greater than or less between than 3 and 2.