Wavelength in an electron transition

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SUMMARY

The discussion centers on the allowed electron transition from the 4p to 4s orbital in sodium (Z = 11) and the calculation of its wavelength. The transition is confirmed as allowed due to the change in angular momentum quantum number (Δl = 1). The energy difference (ΔE) is calculated using the formula E_n = -13.60/n² eV, leading to a wavelength of 2.21 μm for the transition. The participants also reference the need for effective nuclear charge considerations in energy calculations.

PREREQUISITES
  • Understanding of quantum mechanics and electron transitions
  • Familiarity with the energy level formula E_n = -13.60/n² eV
  • Knowledge of angular momentum quantum numbers and their significance
  • Basic grasp of effective nuclear charge concepts in atomic physics
NEXT STEPS
  • Research the concept of effective nuclear charge and its impact on electron transitions
  • Learn about the selection rules for allowed and forbidden transitions in quantum mechanics
  • Explore the derivation and application of the wavelength formula λ = 1240 eV nm / ΔE
  • Investigate the energy level diagrams for sodium and other alkali metals
USEFUL FOR

Students and professionals in physics, particularly those studying atomic structure and electron transitions, as well as educators teaching quantum mechanics concepts.

elephantorz
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1. Is a 4p -> 4s transition allowed in sodium? If so, what is the wavelength? If not, why not? (Z = 11 for sodium)



2. \Deltal = |l2 - l1| = 1
That is for the first question, in which case it is allowed, hence |0-1| = |-1| = 1, and meets the requirements for the equation.

The second part is what I don't understand because I used these equations:
E_{n} = \frac{-13.60}{n^{2}}eV
n = 1, 2, 3, ...


Next I used:
\DeltaE_{atom} = E_{1} - E_{2} = 0

Meaning, I get zero for this because of the repeating n = 4, then 4^{2} which = 16 and therefore I have an issue here I do not know how to solve after pondering.

The third equation I must use is:
\lambda = 1240 eV nm / \DeltaE

But I am not there yet...


3. As you can see my attempt is either erroneous or there is some sort of lone energy I am not aware of, by the way, the answer to this is:

Yes; 2.21 \mum

Thank you.
 
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Ummm... Are you sure it is 4p to 4s? Double check what is written.
 
nickjer said:
Ummm... Are you sure it is 4p to 4s? Double check what is written.

I did, three times...I guess I will just have to lose points for this.
 
Is there a table in your book of the orbital dependence of the energy in sodium?
 
Here is an equation that uses different effective nuclear charges depending on the orbital quantum number:

http://physics.wm.edu/~inovikova/phys251/manual/naspec.pdf
 
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