An atom is in ground state and then absorbs a 12 eV photon. A short while later this atom emits a photon of a different energy (and different wavelength), what are the possible wavelengths of this photon?
An atom is in ground state and then absorbs a 12 eV photon. A short while later this atom emits a photon of a different energy (and different wavelength), what are the possible wavelengths of this photon?
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Please answer part D.
**Energy Level Diagram Explanation:**
- The y-axis represents the Principal Quantum Number.
- The x-axis denotes Energy levels (in electron volts, eV).
- Various arrows indicate transitions between energy levels, labeled A through E.
- Energy levels depicted:
- \( n = 4 \) at \( -3 \, \text{eV} \)
- \( n = 3 \) at \( -5 \, \text{eV} \)
- \( n = 2 \) at \( -8 \, \text{eV} \)
- \( n = 1 \) at \( -15 \, \text{eV} \)
##### Questions:
**(a) Which transition(s) corresponds to photons in the visible spectrum?**
Visible light typically has wavelengths between approximately 400 nm to 700 nm. To determine which transitions correspond to the visible spectrum, we would calculate the energy change (ΔE) for each transition and then use the relation:
\[ \Delta E = \frac{1240}{\lambda (\text{nm})} \]
We'd then check which ΔE falls within the energy range corresponding to visible light (approximately 1.77 eV to 3.10 eV).
From the diagram:
- Transition C: \( 4 \rightarrow 3 \): \( -3 \, \text{eV} \rightarrow -5 \, \text{eV} \) (\( \Delta E = 2 \, \text{eV} \))
This is within the visible spectrum.
Thus, **transition C** could correspond to photons in the visible spectrum.
**(b) Which transition corresponds to having a photon with the longest wavelength?**
The transition with the smallest energy change (ΔE) will correspond to the longest wavelength since \( \lambda \propto \frac{1}{\Delta E} \).
- Transition C: \( 4 \rightarrow 3 \): \( \Delta E = 2 \, \text{eV} \)
- Transition B: \( 3 \rightarrow](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cae87f4-2a03-4d28-9386-4b0284900cdd%2F755e36e1-9fad-48bc-96a3-3fd71386662c%2F8qq2oun_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Energy Level Diagrams
#### Question 9.
The figure below depicts an energy level diagram for a specific atom (non-hydrogen). Multiple transitions are illustrated and labeled by letters. Please keep in mind that the diagram is not drawn to scale.
**Energy Level Diagram Explanation:**
- The y-axis represents the Principal Quantum Number.
- The x-axis denotes Energy levels (in electron volts, eV).
- Various arrows indicate transitions between energy levels, labeled A through E.
- Energy levels depicted:
- \( n = 4 \) at \( -3 \, \text{eV} \)
- \( n = 3 \) at \( -5 \, \text{eV} \)
- \( n = 2 \) at \( -8 \, \text{eV} \)
- \( n = 1 \) at \( -15 \, \text{eV} \)
##### Questions:
**(a) Which transition(s) corresponds to photons in the visible spectrum?**
Visible light typically has wavelengths between approximately 400 nm to 700 nm. To determine which transitions correspond to the visible spectrum, we would calculate the energy change (ΔE) for each transition and then use the relation:
\[ \Delta E = \frac{1240}{\lambda (\text{nm})} \]
We'd then check which ΔE falls within the energy range corresponding to visible light (approximately 1.77 eV to 3.10 eV).
From the diagram:
- Transition C: \( 4 \rightarrow 3 \): \( -3 \, \text{eV} \rightarrow -5 \, \text{eV} \) (\( \Delta E = 2 \, \text{eV} \))
This is within the visible spectrum.
Thus, **transition C** could correspond to photons in the visible spectrum.
**(b) Which transition corresponds to having a photon with the longest wavelength?**
The transition with the smallest energy change (ΔE) will correspond to the longest wavelength since \( \lambda \propto \frac{1}{\Delta E} \).
- Transition C: \( 4 \rightarrow 3 \): \( \Delta E = 2 \, \text{eV} \)
- Transition B: \( 3 \rightarrow
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