Which photon has the higher frequency?

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Discussion Overview

The discussion revolves around the transitions of a hydrogen atom between energy states, specifically from n=3 to n=2 and n=2 to n=1, and the corresponding frequencies of the emitted photons. Participants explore the relationship between quantum states, energy levels, and photon frequency, touching on concepts from both chemistry and physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about the meaning of the principal quantum number "n" and its relationship to energy levels.
  • Others explain that energy levels differ based on the inverse square of the principal quantum number, leading to varying energies for different states.
  • One participant questions whether the energy differences between states n=1, 2, and 3 are constant or not.
  • Another participant clarifies that moving to a state closer to the nucleus results in energy release, prompting discussions about how to calculate energy changes during transitions.
  • There is a discussion about the correct approach to subtracting energy values to determine the energy released as light during transitions.
  • Some participants express confusion about the signs of energy changes and how they relate to the emitted photons.
  • A later reply confirms that the energy change from n=3 to n=2 is negative, indicating energy loss to the emitted photon.
  • Participants also discuss the implications of energy conservation in the context of photon emission during electron transitions.
  • One participant concludes that more energy is released during the transition from n=2 to n=1 compared to n=3 to n=2, although this is not universally agreed upon.

Areas of Agreement / Disagreement

There is no clear consensus on the exact energy differences between the transitions or the implications for photon frequency, as participants express varying degrees of understanding and interpretation of the energy calculations involved.

Contextual Notes

Participants rely on different interpretations of energy calculations and the relationship between quantum states, which may lead to confusion regarding the signs and values of energy changes. The absence of a textbook or formal resources contributes to the uncertainty in the discussion.

smokie
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Chemistry is not my strong subject...

A hydrogen atom undergoes a transition from the state n=3 to n=2 and then another transition from n=2 to n=1. Two photons are created due to these processes. Which photon has the higher frequency?

AND What is meant by 'n = #' ?
 
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Check out this thread, keeping in mind that [tex]E=h\nu[/tex]. The principal quantum number, "n", is a property of a quantum mechanical state with certain energy. States with different "n" have different energies.
 
I didn't understand the discussion on that site very well. The course I'm in is a physics course and they threw in some chemistry, however, we don't have a textbook, so my resource is mainly the internet...

States with different 'n' values have different energies, but do the energies from n = 1, 2, 3 differ by a constant value [i.e. 1, 3, 5] or not?
 
smokie said:
States with different 'n' values have different energies, but do the energies from n = 1, 2, 3 differ by a constant value [i.e. 1, 3, 5] or not?

Actually, the energy of a state is proportional to the square of the inverse of the principal quantum number, "n". So, if we choose units in which the energy of the n=1 state is -1 (the total energy of a bound state is always negative), then the n=2,3, and 4 states will have energies of -1/4, -1/9, and -1/16, respectively. An energy greater than 0 will mean that the electron is no longer bound to the nucleus.
 
ok got that...so then obviously an electron moving from energy state -1/9 to -1/4, it would give off more energy than one moving from -1/4 to -1, correct?
 
smokie said:
ok got that...so then obviously an electron moving from energy state -1/9 to -1/4, it would give off more energy than one moving from -1/4 to -1, correct?

You might want to try that subtraction again. :wink:
 
Well I can see what I did wrong but doesn't an electron moving to a state 'closer' to the nucleus give off energy?
 
smokie said:
Well I can see what I did wrong but doesn't an electron moving to a state 'closer' to the nucleus give off energy?

If by "closer" you mean more tightly bound to the nucleus, then yes. The most tightly bound state is n=1.
 
Yes, what I mean is that the electrons are more tightly bound to the nucleus. So, how should I do my subtraction? I should do -1/4 - -1/9 ? <-- Negative number would be required for energy released... ?
 
Last edited:
  • #10
smokie said:
Yes, what I mean is that the electrons are more tightly bound to the nucleus. So, how should I do my subtraction? I should do -1/4 - -1/9 ? <-- Negative number would be required for energy released... ?

When it moves from state n=3 to n=2, does the electron's energy increase or decrease (based on what I already said)? If energy is conserved, what does this mean for the photon that's emitted?
 
  • #11
When moving from state n = 3 to n = 2, the electron's energy decreases... it loses some of the energy to the escaping photon...that's what I'm understanding..
 
  • #12
smokie said:
When moving from state n = 3 to n = 2, the electron's energy decreases... that's what I'm understanding..

That's right. So, to conserve energy, the atom must emit a photon of light!
 
  • #13
Exactly, soo, but then isn't my subtraction correct?

The only thing I'm seeing wrong with my subtraction is that for 'energy' I should have a negative answer...
 
  • #14
In our units, the energy change from n=3 to n=2 is (-1/9)-(-1/4)=5/36. This is the energy that's released as light. It's the change in energy of the electron that's negative: (-1/4)-(-1/9)=-5/36.
 
  • #15
Ahh, I see what you mean. E2 - E1 = energy released as light, while E1 - E2 = change in energy of the electron.
 
  • #16
That would mean that more energy is released from n = 2 to n = 1, than is from n = 3 to n = 2, would it not?
 

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