Hydrogen electron transition intensity 2p - 1s

In summary, the conversation discusses a transition from state 2p to 1s of an electron in a hydrogen atom and the intensity of radiation emitted by the electron. It is mentioned that this transition is not allowed due to a computation error, but it is actually allowed in the literature and logically. The issue may be related to the polarization of the photon and the use of spherical harmonics in the calculations.
  • #1
FrostInMyTeeth
1
0
Let's say we have a transition from state 2p to 1s of an hydrogen atom's electron. The intensity radiated by the electron is given by I = 4/3 ωfi4 e2/c3 |< f | r | i >|2.

If we take the the | 2 1 1 > → | 1 0 0 > transition for example, we must compute the following integral :

< f | r | i > = C1 ∫∫∫ e-r/a r sin(θ) ei*Φ * e-r/2a sin(theta) r2 sin(θ)dr dθ dΦ

, r = [ 0→ ∞], θ = [0 → pi], Φ = [0 → 2π]

Which can be separated in three integrals (depending on r, θ and Φ respectively). The integral in Φ is

IΦ = ∫ ei*Φ dΦ = 0

, Φ = [0 → 2π]

Which means that < f | r | i > = 0 and that the transition is not allowed. However in the literature (and logically), this transition is allowed.

I'm not quite sure if it's a comprehension issue or a simple computation error.

Thank you !
 
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  • #2
You forgot the polarization of the photon. The term in the middle of the integral is not simply r, but ##\mathbf{r} \cdot \mathbf{\epsilon}##. That will add an angular compnent, which can be expressed in terms of ##Y_{1,0}##, ##Y_{1,+1}##, or ##Y_{1,-1}##. The angular part is then the integral of three spherical harmonics.
 

Related to Hydrogen electron transition intensity 2p - 1s

1. What is the significance of the hydrogen electron transition intensity 2p - 1s?

The hydrogen electron transition intensity 2p - 1s refers to the amount of energy released or absorbed when an electron moves from the 2p orbital to the 1s orbital in a hydrogen atom. This transition is important in understanding the behavior of light and the structure of atoms.

2. How is the intensity of the hydrogen electron transition measured?

The intensity of the hydrogen electron transition is typically measured through spectroscopy, which involves analyzing the spectrum of light emitted or absorbed by the hydrogen atom. The intensity can also be calculated using mathematical equations and experimental data.

3. What factors affect the intensity of the hydrogen electron transition?

The intensity of the hydrogen electron transition is influenced by several factors, including the energy difference between the 2p and 1s orbitals, the number of hydrogen atoms present, and the temperature and pressure of the environment. Additionally, the presence of other elements or molecules can also affect the intensity.

4. What does a higher intensity of the hydrogen electron transition indicate?

A higher intensity of the hydrogen electron transition indicates a higher probability of an electron transitioning from the 2p to the 1s orbital. This can occur due to an increase in energy, such as through the absorption of light, or a decrease in energy, such as through the emission of light.

5. How does the intensity of the hydrogen electron transition relate to the colors of light emitted or absorbed?

The intensity of the hydrogen electron transition is directly related to the colors of light that are emitted or absorbed. Higher intensities correspond to more energetic transitions and therefore shorter wavelengths of light, which appear as more blue or violet in color. Lower intensities correspond to less energetic transitions and longer wavelengths of light, which appear as more red or orange in color.

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