Kinetic Enegry and Hydrogen atoms

AI Thread Summary
The minimum kinetic energy required to ionize a hydrogen atom is 13.6 eV. When electrons with 12.8 eV energy collide with hydrogen atoms, they can excite the atoms to a specific energy level, denoted as n_0. The discussion highlights that the energy levels of hydrogen are calculated using the formula -13.6 eV/n^2, and the energy differences between levels can be used to determine the energies of emitted photons. The conversation also emphasizes the complexity of photon energies due to atomic motion and collisions, leading to a continuum rather than discrete values. Ultimately, the participants clarify the calculations needed for various photon energies based on transitions between excited states.
lebprince
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Homework Statement



a) What is the minimum kinetic energy in electron volts that an electron must have to be able to ionize a hydrogen atom (that is, remove the electron from being bound to the proton)? I got the answer here which is 13.6 ev

b) If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?
b-1)Energy of highest-energy photon: I got the answer here which is 12.8
b-2)Energy of next highest-energy photon:
b-3)Energy of next highest-energy photon:
b-4)Energy of next highest-energy photon:
b-5)Energy of next highest-energy photon:
b-6)Energy of lowest-energy photon:


I Just need help with ( b-2 to b-6) Thanks
 
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The answer depends on details of your solution to b-1. In particular, what energy level (n value) is the Hydrogen excited to by the 12.8 eV energy?
 
Redbelly98 said:
The answer depends on details of your solution to b-1. In particular, what energy level (n value) is the Hydrogen excited to by the 12.8 eV energy?

am sorry but that 12.8 was a guess for b-1 and i don't know how to find that.
 
Question (b) is a bad question: the energies of the photons emitted by an actual gas form a continuum because of the motion of the atoms, their collisions, and the fact the excited states are unstable. So you can't even talk about the energy of the "next highest-energy" photon.

But setting that aside, what is meant here, no doubt, is that the 12.8 eV brings you to a particular excited state with a certain value of n, call it n_0 (easy to calculate). From n_0 the atom could make a transition to the ground state, giving back a 12.8 eV photon. But it could also make a transition to the n=2 state, emitting a less energetic photon. It could also "fall" to the n=3 state, emitting an even less energetic photon. And, once an atom is in the n=3 state, it could fall to the ground state from there, emitting yet another photon...etc.
 
borgwal said:
Question (b) is a bad question: the energies of the photons emitted by an actual gas form a continuum because of the motion of the atoms, their collisions, and the fact the excited states are unstable. So you can't even talk about the energy of the "next highest-energy" photon.

But setting that aside, what is meant here, no doubt, is that the 12.8 eV brings you to a particular excited state with a certain value of n, call it n_0 (easy to calculate). From n_0 the atom could make a transition to the ground state, giving back a 12.8 eV photon. But it could also make a transition to the n=2 state, emitting a less energetic photon. It could also "fall" to the n=3 state, emitting an even less energetic photon. And, once an atom is in the n=3 state, it could fall to the ground state from there, emitting yet another photon...etc.

so is there a specific formula i should use to calculate these answers?
 
Yes...don't you know a formula for the energies of hydrogen levels, as a function of "n"?

The question clearly assumes you know this, so look it up in your textbook!
 
borgwal said:
Yes...don't you know a formula for the energies of hydrogen levels, as a function of "n"?

the formula i know is -13.6/n^2 oh so instead of 13.6 i would use 12.8?
 
lebprince said:
the formula i know is -13.6/n^2 oh so instead of 13.6 i would use 12.8?

No, it is and remains -13.6eV/n^2.
 
Hint: the ground state corresponds to n=1. How much energy difference is there between n=1 and n=2?

You want to find a n_0 such that the difference between the levels n_0 and n=1, is about 12.8 eV.
 
  • #10
borgwal said:
Hint: the ground state corresponds to n=1. How much energy difference is there between n=1 and n=2?

You want to find a n_0 such that the difference between the levels n_0 and n=1, is about 12.8 eV.

so n0 - n1 = 12.8 and n1 is -13.6 so n0= 12.8-13.6 = -0.8
 
  • #11
Do you understand the equation that says the energy of level n is -13.6eV/n^2?
 
  • #12
borgwal said:
Do you understand the equation that says the energy of level n is -13.6eV/n^2?

it doesn't look like it cause the teacher we have is horrible. i barely understand the question sorry.
 
  • #13
It says the energy of level n=1 is -13.6 eV, for n=2 the energy is -13.6/4=-3.4 eV, etc.
So the difference in energy between these two levels is (-3.4--13.6)eV=10.2 eV.

Now find n_0 such that -13.6/n_0^2+13.6=12.8 eV.
 
  • #14
borgwal said:
It says the energy of level n=1 is -13.6 eV, for n=2 the energy is -13.6/4=-3.4 eV, etc.
So the difference in energy between these two levels is (-3.4--13.6)eV=10.2 eV.

Now find n_0 such that -13.6/n_0^2+13.6=12.8 eV.

ok so n0^2= 13.6/0.8 = 17 then sqrt 17 = 4.12 which n0
 
  • #15
Yes, so presumably n=4 is meant as the level in which the hydrogen atoms end up (n can only be an integer!)
 
  • #16
borgwal said:
Yes, so presumably n=4 is meant as the level in which the hydrogen atoms end up (n can only be an integer!)

ok good so for b-2 i would use n= 3 so -13.6/9+13.6 and that gave me 12.089
for b-3 n=2 so i would get 10
b-4 i would use n=1 so now i would get 0 which gave me a wrong answer the first 2 were right how come
 
  • #17
You can go from n=4 to n=2 also
 
  • #18
borgwal said:
You can go from n=4 to n=2 also

so i should get the same 3 answer again? if so its not working.
 
  • #19
No, your b-3 answer is for n=2 to n=1.
 
  • #20
borgwal said:
No, your b-3 answer is for n=2 to n=1.

ok so for b-4 i would repeate the same steps. start at n=4 so i will get 12.8 again, and for b-5 i would get 10 again and for b-6 i would get 12? is that right?
 
  • #21
No, of course not. What's the energy difference between levels n=4 and n=2?
 
  • #22
borgwal said:
No, of course not. What's the energy difference between levels n=4 and n=2?

its -13.6/16 + 13.6/4 = 2.55
 
  • #23
try that as answer b-4...
 
  • #24
also calculate the energy differences between n=4 and n=3, as well as between n=3 and n=2, that should give you answers b-6 and b-5, respectively.
 
  • #25
borgwal said:
also calculate the energy differences between n=4 and n=3, as well as between n=3 and n=2.

Thanks a lot for all your help. i really appreciate
 
  • #26
lebprince said:
Thanks a lot for all your help. i really appreciate

i got it thanks
 
  • #27
Good!
 

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