Bohr Model: Energy Jump in Hydrogen Atom

In summary, the conversation discusses the energy changes that occur when an electron jumps between different orbits in a Hydrogen atom. The calculations show that the transition from the second orbit to the first one releases the most potential energy, but for a transition of the type n+1 to n, the transition from 2 to 1 has the largest energy change. This may seem counterintuitive, but it can be verified using the Rydberg formula. The conversation also touches on the false idea of relating energy levels to orbit radii in atomic shells.
  • #1
hav0c
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Am I right in saying that in a Hydrogen atom when an electron jumps from the second orbit to the first one the energy change is more than any other possible jump (when the jump is not to the first orbit). The calculations seem to support me but it doesn't feel right.
 
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  • #2
hav0c said:
Am I right in saying that in a Hydrogen atom when an electron jumps from the second orbit to the first one the energy change is more than any other possible jump (when the jump is not to the first orbit). The calculations seem to support me but it doesn't feel right.
Why does it not feel right?
What calculations seem to support you and how?

The transition from continuum to the n=1 shell (the "first one") releases the most potential energy, but for a transition of the type n+1 to n, the transition 2->1 has the largest energy change.
You should be able to verify this from the Rydberg formula.
 
  • #3
Simon Bridge said:
Why does it not feel right?
What calculations seem to support you and how?

The transition from continuum to the n=1 shell (the "first one") releases the most potential energy, but for a transition of the type n+1 to n, the transition 2->1 has the largest energy change.
You should be able to verify this from the Rydberg formula.
this is exactly what i am getting, but thinking logically shouldn't the transition from n=∞ to n=2 produce a greater energy change?(than n=2 to n=1)
Also wouldn't this imply that to ionize an atom from the second shell the energy required is atleast less than half than that to ionize it from the first shell?
 
  • #4
hav0c said:
but thinking logically shouldn't the transition from n=∞ to n=2 produce a greater energy change?(than n=2 to n=1)

Can you describe the logic?
 
  • #5
well since energy increases as distance from nucleus increases and the energy gap b/w consecutive orbits decreases, it seems to me that if what i am saying is true, then distance b/w n=1 and n=2 should be greater than n=2 to n=∞, which is wrong.
Edit: thanks a lot i got my mistake
Edit 2: this is true right?Also wouldn't this imply that to ionize an atom from the second shell the energy required is atleast less than half than that to ionize it from the first shell?
 
  • #6
The transition inf->2 is not a transition of form n+1 -> n; but never mind.

The energy changes are proportional to the difference in the reciprocal of the squares of the start and finish quantum numbers.

transition from inf->2 would be proportional to |0-1/4|=1/4
transition from 2->1 would be proportional to |1-1/4|=3/4
(notice how taking 1/4 from 0 gets a smaller number than taking 1/4 from 1?)

simiarly:
transition from inf->3 would be proportional to 1/9
transition from 3->1 would be proportional to 8/9

i.e. the energy levels tend to cluster close to the continuum level. re:

hyd_levels.gif


I think you are confusing energy levels with orbit radii.
You should not be picturing radii at all in connection with atomic shells: it is a completely false picture.
 
Last edited:
  • #7
hav0c said:
this is exactly what i am getting, but thinking logically shouldn't the transition from n=∞ to n=2 produce a greater energy change?(than n=2 to n=1)

Imagine an enormous flat plain at 100 meters above sea level. In the middle of this plain there's a shallow depression; the bottom of the depression is 90 meters above sea level. And then right at the low point of this depression someone has drilled a well 500 meters into the ground.

Send a 1kg ball rolling from infinity to the bottom of the depression and it will drop 10 meters with energy change ##mgh## equal to 100 Joules; that's the transition from n=∞ to n=2. But when it falls to the bottom of the well (n=2 to n=1) it will pick up another 5000 Joules.
 
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  • #8
Simon Bridge said:
The transition inf->2 is not a transition of form n+1 -> n; but never mind.

The energy changes are proportional to the difference in the reciprocal of the squares of the start and finish quantum numbers.

transition from inf->2 would be proportional to |0-1/4|=1/4
transition from 2->1 would be proportional to |1-1/4|=3/4
(notice how taking 1/4 from 0 gets a smaller number than taking 1/4 from 1?)

simiarly:
transition from inf->3 would be proportional to 1/9
transition from 3->1 would be proportional to 8/9

i.e. the energy levels tend to cluster close to the continuum level. re:

hyd_levels.gif


I think you are confusing energy levels with orbit radii.
You should not be picturing radii at all in connection with atomic shells: it is a completely false picture.
Thanks a lot i was not considering the decrease in effective charge. that's why i wasn't able to understand the numbers
 
  • #9
hav0c said:
Thanks a lot i was not considering the decrease in effective charge. that's why i wasn't able to understand the numbers
The "effective charge" of a nucleus is usually due to inner-shell electrons screening the nuclear charge from the outer shell electrons. That is different from what you are talking about: the electron still sees the entire +e charge from the nucleus no matter what it's energy level.

[BTW: thanks for spotting the typo - edited in original]
 
  • #10
When the theory conflicts with your intuition, it's time to fix the intuition! (well, actually, intuition is a very useful guiding force, but in this case it's wrong)
 

1. What is the Bohr Model?

The Bohr Model is a simplified model of the atom proposed by Niels Bohr in 1913. It depicts the atom as a small, positively charged nucleus surrounded by electrons in specific energy levels or orbits.

2. What is an energy jump in a hydrogen atom?

An energy jump, also known as an energy transition, is when an electron in a hydrogen atom moves from one energy level to another. This is accompanied by the absorption or emission of a photon of light.

3. How does the Bohr Model explain energy jumps in a hydrogen atom?

The Bohr Model states that electrons in a hydrogen atom can only exist in specific energy levels, and they can jump from one level to another by absorbing or emitting energy in the form of photons. The energy of the photon is equal to the energy difference between the two levels.

4. Why is the Bohr Model important?

The Bohr Model was the first successful attempt to explain the structure and behavior of atoms. It laid the foundation for further advancements in atomic theory and helped scientists understand the relationship between energy and light.

5. Are energy jumps in a hydrogen atom quantized?

Yes, energy jumps in a hydrogen atom are quantized, meaning they can only occur in specific amounts or levels. This is in line with the Bohr Model's concept of electron energy levels and is supported by experimental evidence.

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