Wavelength in an electron transition

In summary, the conversation is about the transition from the 4p to 4s orbital in sodium. The wavelength for this transition is 2.21 μm. There is some confusion about the equations used, but it is determined that the transition is allowed and meets the requirements for the equation. The conversation also mentions the use of effective nuclear charges in different orbital quantum numbers.
  • #1
1. Is a 4p -> 4s transition allowed in sodium? If so, what is the wavelength? If not, why not? (Z = 11 for sodium)



2. [tex]\Delta[/tex]l = |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:
[tex]E_{n}[/tex] = [tex]\frac{-13.60}{n^{2}}[/tex]eV
n = 1, 2, 3, ...


Next I used:
[tex]\Delta[/tex]E[tex]_{atom}[/tex] = E[tex]_{1}[/tex] - E[tex]_{2}[/tex] = 0

Meaning, I get zero for this because of the repeating n = 4, then 4[tex]^{2}[/tex] 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:
[tex]\lambda[/tex] = 1240 eV nm / [tex]\Delta[/tex]E

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 [tex]\mu[/tex]m

Thank you.
 
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  • #2
Ummm... Are you sure it is 4p to 4s? Double check what is written.
 
  • #3
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.
 
  • #4
Is there a table in your book of the orbital dependence of the energy in sodium?
 
  • #5
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 [Broken]
 
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1. What is a "wavelength" in an electron transition?

A wavelength in an electron transition refers to the distance between two consecutive peaks or troughs of an electromagnetic wave that is emitted or absorbed during the transition of an electron between energy levels. It is commonly measured in units of nanometers (nm) or angstroms (Å).

2. How does the wavelength of an electron transition relate to its energy?

The wavelength of an electron transition is inversely proportional to the energy of the transition. This means that as the wavelength decreases, the energy of the transition increases, and vice versa. This relationship is described by the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

3. What factors influence the wavelength of an electron transition?

The wavelength of an electron transition is primarily determined by the energy difference between the two energy levels involved in the transition. Other factors that may influence the wavelength include the type of atom or molecule, the presence of external electric or magnetic fields, and relativistic effects.

4. Can the wavelength of an electron transition be calculated?

Yes, the wavelength of an electron transition can be calculated using the Rydberg formula, which is given by 1/λ = R(1/n2 - 1/m2), where λ is the wavelength, R is the Rydberg constant, and n and m are the principal quantum numbers of the initial and final energy levels, respectively.

5. How is the wavelength of an electron transition observed?

The wavelength of an electron transition can be observed through spectroscopy techniques, such as absorption or emission spectroscopy. These methods involve passing light through a sample of atoms or molecules and analyzing the resulting spectrum to determine the wavelengths of the transitions that occurred.

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