mirror of
https://asciireactor.com/otho/as-500.git
synced 2024-11-21 23:15:05 +00:00
24 lines
786 B
Plaintext
24 lines
786 B
Plaintext
|
Old approach:
|
|||
|
|
|
|||
|
|
|
|||
|
|
4πj(u,l) = nᵤ (Aᵤₗ + qᵤₗ nₑ) hν.
|
|||
|
|
|
|||
|
|
Let's ignore collisional excitement, making
|
|||
|
|
|
|||
|
|
4πj(u,l) = n₂ Aᵤₗ hν.
|
|||
|
|
|
|||
|
|
From Allen, Table 4.11,
|
|||
|
|
|
|||
|
|
A[Hβ] = 8.419 × 10⁶ s⁻¹
|
|||
|
|
|
|||
|
|
If H was totally ionized this would be 0, right? Thought I could maybe find a recombination balance to determine a better ratio, but assuming H is not ionized seems to be the approach other students are taking.
|
|||
|
|
|
|||
|
|
From the Boltzman factors computed for hydrogen in hw14, I just reused my spreadsheet to find n₂ = (Z₂/∑Zᵢ * nₜₒₜ) at T=1e4 K:
|
|||
|
|
|
|||
|
|
n₂ = 0.275 [cm⁻³].
|
|||
|
|
|
|||
|
|
hν = 4.09 × 10⁻¹² [ergs].
|
|||
|
|
|
|||
|
|
4πj(u,l) = n₂ Aᵤₗ hν
|
|||
|
|
= 0.275 [cm⁻³] 8.419 × 10⁶ [s⁻¹] 4.09 × 10⁻¹² [ergs]
|
|||
|
|
*** = 9.47 × 10⁻⁶ [ergs cm⁻³ s⁻¹].
|