---
# Chapter 6: Symbols, Nebular Lines and electronic configurations


```{tableofcontents}
```

## Symbols

*   α Recombination coefficient ({math}`\alpha_{B}` is for Case B)

*   ε emissivity

*   θ angle (spatial resolution or grating)

*   {math}`\kappa_{\nu}` Absorption coefficient

*   λ Wavelength

*   μ Reduced mass

*   ν Frequency

*   {math}`\rho_{\nu}` Radiation field energy density

*   {math}`\sigma_{\nu}` Absorption cross section

*   τ Radiative lifetime

*   {math}`\tau_{\lambda}` Optical depth

*   Υ Effective collision strength

*   {math}`\chi_{\rm ion}` ionization energy

*   Ω Collisional strength

<!---->

*   {math}`a_{0}` Bohr radius

*   {math}`A_{\lambda}` Dust extinction at wavelength λ

*   {math}`A_{ul}` Einstein A (spontaneous) coefficient

*   {math}`B_{lu}` Einstein B (stimulated) coefficient

*   {math}`B_{\nu}` Planck formula

*   {math}`c` Speed of light

*   {math}`c_{H\beta}` Extinction coefficient (for nebulae)

*   {math}`C_{lu}` Collisional excitation rate

*   {math}`d` distance (to source) or separation (between slits)

*   {math}`D` diameter of telescope

*   {math}`E` Energy (above ground state)

*   {math}`E_{\rm B-V}` colour excess

*   {math}`f_{ul}` Oscillator strength

*   {math}`F` line flux or total angular momentum of atom

*   {math}`F_{\rm cam}` Focal length of camera

*   {math}`g` Statistical weights (or degeneracies)

*   {math}`\mathcal{G}` energy input rate

*   {math}`h` Planck’s constant

*   {math}`H_{0}` Hubble constant

*   {math}`I` intensity or nuclear spin quantum number

*   {math}`j` total angular momentum of electron ({math}`J` sum in outer shell)

*   {math}`J` number of stellar photons

*   {math}`k` Boltzmann constant

*   {math}`l` Electron orbital angular momentum ({math}`L` sum in outer shell)

*   {math}`L` luminosity

*   {math}`\mathcal{L}` Energy loss rate

*   {math}`m_{e}` Electron mass

*   {math}`m_{p}` Proton mass

*   {math}`M` magnification of telescope

*   {math}`n` Diffraction grating order or principal quantum number

*   {math}`n_{c}` Critical density

*   {math}`n_{e}` Electron density

*   {math}`n_{H}` Hydrogen density

*   {math}`N(H)` column density of hydrogen atoms

*   {math}`N` number of lines in grating

*   {math}`N2` Ratio of nebular lines (for abundance estimates)

*   {math}`N_{\rm O7V}` Number of O7V stars

*   {math}`O3N2` Ratio of nebular lines (for abundance estimates)

*   {math}`p` Parity

*   {math}`Q_{0}` Number of hydrogen ionizing photons

*   {math}`Q_{1}` Number of singly ionizing photons of He

*   {math}`Q_{2}` Number of doubly ionizing photons of He

*   {math}`Q_{\rm ext}` Efficiency factor of extinction

*   {math}`R` resolving power

*   {math}`R_{23}` Ratio of strong nebular lines (for abundance estimates)

*   {math}`R_{V}` ratio of visual extinction to colour excess

*   {math}`R_{\infty}` Rydberg energy

*   {math}`\mathcal{R}_{s}` Strömgren radius

*   {math}`s` Spin angular momentum ({math}`S` sum in outer shell)

*   {math}`T` temperature ({math}`T_{e}` electron, {math}`T_{\ast}` stellar)

*   {math}`v_{\rm r}` radial velocity ({math}`v_{\rm turb}` turbulent velocity)

*   {math}`W` grating width

*   {math}`W_{\lambda}` Equivalent width

*   {math}`x_{\lambda}` coefficient of extinction at wavelength λ vs V-band

*   {math}`z` redshift or zenith distance

+++
## Common nebular lines

:::{list-table} Selected nebular emission lines in H  ii regions and Planetary Nebulae in the UV and optical,
:header-rows: 0
:name: uv_optical_lines
:align: center

*   *   λ

         (Å)

    *   Ion

    *   Transition

*   *   1032,1038

    *   O  vi

    *   {math}`2s ^{2}`
        S - 
        {math}`2p ^{2}`
        P
        °

*   *   1238,1242

    *   N  v

    *   {math}`2s ^{2}`
        S - 
        {math}`2p ^{2}`
        P
        °

*   *   1486

    *   N  iv]

    *   {math}`2s^{2} \hspace{1mm} ^{1}`
        S - 
        {math}`2p ^{3}`
        P
        °

*   *   1548,1551

    *   C  iv

    *   {math}`2s ^{2}`
        S - 
        {math}`2p ^{2}`
        P
        °

*   *   1640

    *   He  ii

    *   3–2

*   *   1663

    *   O  iii]

    *   {math}`2p^{2} \hspace{1mm} ^{3}`
        P - 
        {math}`2p^{3} \hspace{1mm} ^{5}`
        P
        °

*   *   1747,1754

    *   N  iii]

    *   {math}`2p^{2} \hspace{1mm} ^{4}`
        P - 
        {math}`2p \hspace{1mm} ^{2}`
        P
        °

*   *   1907,1909

    *   C  iii]

    *   {math}`2s^{2} \hspace{1mm} ^{1}`
        S - 
        {math}`2p ^{3}`
        P
        °

*   *   2297

    *   C  iii

    *   {math}`2p  ^{1}`
        P
        {math}`^{\circ} - 2p^{2} \hspace{1mm} ^{1}`
        D

*   *   2323,2328

    *   C  ii]

    *   {math}`2p^{2} \hspace{1mm} ^{4}`
        P - 
        {math}`2p \hspace{1mm} ^{2}`
        P
        °

*   *   2796,2803

    *   Mg  ii

    *   {math}`3p ^{2}`
        P
        {math}`^{\circ} - 3s ^{2}`
        S

*   *   3726,3729

    *   \[O  ii]

    *   {sup}`2`
        D - S
        {math}`_{3/2}`

*   *   3868,3967

    *   \[Ne  iii]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P

*   *   3970

    *   H  i

    *   7–2

*   *   4101

    *   H  i

    *   6–2

*   *   4340

    *   H  i

    *   5–2

*   *   4363

    *   \[O  iii]

    *   {sup}`1`
        S
        {math}`_{0} - ^{1}`
        D
        {sub}`2`

*   *   4471

    *   He  i

    *   {math}`4d \hspace{1mm}^{3}`
        D - 
        {math}`2p \hspace{1mm} ^{3}`
        P

*   *   4686

    *   He  ii

    *   4–3

*   *   4861

    *   H  i

    *   4–2

*   *   4959,5007

    *   \[O  iii]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P

*   *   5755

    *   \[N  ii]

    *   {sup}`1`
        S
        {math}`_{0} - ^{1}`
        D
        {sub}`2`

*   *   5876

    *   He  i

    *   {math}`3d \hspace{1mm} ^{3}`
        D - 
        {math}`2p \hspace{1mm} ^{3}`
        P
        °

*   *   6300,6364

    *   \[O  i]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P

*   *   6548

    *   \[N  ii]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P
        {sub}`1`

*   *   6563

    *   H  i

    *   3–2

*   *   6584

    *   \[N  ii]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P
        {sub}`2`

*   *   6678

    *   He  i

    *   {math}`3d \hspace{1mm} ^{1}`
        D - 
        {math}`2p \hspace{1mm} ^{1}`
        P
        °

*   *   6716,6731

    *   \[S  ii]

    *   {sup}`2`
        D
        {math}`^{\circ} - ^{4}`
        S
        {math}`_{3/2}^{\circ}`

*   *   7065

    *   He  i

    *   {math}`3s \hspace{1mm} ^{3}`
        S - 
        {math}`2p \hspace{1mm} ^{3}`
        P
        °

*   *   7135

    *   \[Ar  iii]

    *   {sup}`1`
        D
        {math}`_{2} - ^{3}`
        P

*   *   7319-7330

    *   \[O  ii]

    *   {sup}`2`
        P
        {math}`^{\circ} - ^{2}`
        D
        °

*   *   9069,9531

    *   \[S  iii]

    *   {sup}`1`
        D
        {sub}`2`
         \- 
        {sup}`3`
        P
:::

:::{list-table} Selected nebular emission lines in H  ii regions and Planetary Nebulae in the IR.
:header-rows: 0
:name: ir_lines
:align: center

*   *   {math}`\lambda (\mu`
        m)

    *   Ion

    *   Transition

*   *   1.012

    *   He  ii

    *   5-4

*   *   1.083

    *   He  i

    *   {math}`2p \hspace{1mm} ^{3}`
        P
        {math}`^{\circ} - 2s \hspace{1mm} ^{3}`
        S

*   *   1.282

    *   H  i

    *   5-3

*   *   1.875

    *   H  i

    *   4-3

*   *   2.058

    *   He  i

    *   {math}`2p \hspace{1mm} ^{1}`
        P
        {math}`^{\circ} - 2s \hspace{1mm} ^{1}`
        S

*   *   2.626

    *   H  i

    *   6-4

*   *   3.09

    *   He  ii

    *   7-6

*   *   4.05

    *   H  i

    *   5-4

*   *   4.65

    *   H  i

    *   7-5

*   *   5.61

    *   \[Mg  v]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`2`

*   *   7.46

    *   H  i

    *   6-5

*   *   7.50

    *   H  i

    *   8-6

*   *   7.65

    *   \[Ne  vi]

    *   {sup}`2`
        P
        {math}`_{3/2}^{\circ} - ^{2}`
        P
        {math}`_{1/2}^{\circ}`

*   *   7.90

    *   \[Ar  v]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`2`

*   *   8.99

    *   \[Ar  iii]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`2`

*   *   10.51

    *   \[S  iv]

    *   {sup}`2`
        P
        {math}`_{3/2}^{\circ} - ^{2}`
        P
        {math}`_{1/2}^{\circ}`

*   *   11.31

    *   H  i

    *   9-7

*   *   12.37

    *   H  i

    *   7-6

*   *   12.81

    *   \[Ne  ii]

    *   {sup}`2`
        P
        {math}`_{1/2} - ^{2}`
        P
        {math}`_{3/2}`

*   *   14.32

    *   \[Ne  v]

    *   {sup}`3`
        P
        {math}`_{2} - ^{3}`
        P
        {sub}`1`

*   *   15.55

    *   \[Ne  iii]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`2`

*   *   18.71

    *   \[S  iii]

    *   {sup}`3`
        P
        {math}`_{2} - ^{3}`
        P
        {sub}`1`

*   *   19.06

    *   H  i

    *   8-7

*   *   24.32

    *   \[Ne  v]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`0`

*   *   25.89

    *   \[O  iv]

    *   {sup}`2`
        P
        {math}`_{3/2}^{\circ} - ^{2}`
        P
        {math}`_{1/2}^{\circ}`

*   *   27.80

    *   H  i

    *   9-8

*   *   33.48

    *   \[S  iii]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`0`

*   *   36.01

    *   \[Ne  iii]

    *   {sup}`3`
        P
        {math}`_{0} - ^{3}`
        P
        {sub}`1`

*   *   37.87

    *   H  i

    *   10-9

*   *   51.81

    *   \[O  iii]

    *   {sup}`3`
        P
        {math}`_{2} - ^{3}`
        P
        {sub}`1`

*   *   57.32

    *   \[N  iii]

    *   {sup}`2`
        P
        {math}`_{3/2} - ^{2}`
        P
        {math}`_{1/2}`

*   *   88.36

    *   \[O  iii]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`0`

*   *   121.9

    *   \[N  ii]

    *   {sup}`3`
        P
        {math}`_{2} - ^{3}`
        P
        {sub}`1`

*   *   157.7

    *   \[C  ii]

    *   {sup}`2`
        P
        {math}`_{3/2} - ^{2}`
        P
        {math}`_{1/2}`

*   *   205.2

    *   \[N  ii]

    *   {sup}`3`
        P
        {math}`_{1} - ^{3}`
        P
        {sub}`0`
:::

+++
## Electronic configurations

:::{list-table} Electronic configuration of the first 20 elements. The inner K shell {math}`(n=1)` is full for helium, L shell ({math}`n=2)` is full for neon, whereas the M shell ({math}`n`=3) is incomplete for potassium and calcium (missing {math}`3d`) despite the N shell ({math}`n=4`) becoming populated.
:header-rows: 0
:name: 20elements
:align: center

*   *   Element

    *   Z

    *   Electronic configuration

*   *   H

    *   1

    *   {math}`1 s`

*   *   He

    *   2

    *   {math}`1 s^{2}`

*   *   Li

    *   3

    *   {math}`1 s^{2} \hspace{2mm} 2 s`

*   *   Be

    *   4

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2}`

*   *   B

    *   5

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2 p`

*   *   C

    *   6

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{2}`

*   *   N

    *   7

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{3}`

*   *   O

    *   8

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{4}`

*   *   F

    *   9

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{5}`

*   *   Ne

    *   10

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6}`

*   *   Na

    *   11

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s`

*   *   Mg

    *   12

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2}`

*   *   Al

    *   13

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p`

*   *   Si

    *   14

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{2}`

*   *   P

    *   15

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{3}`

*   *   S

    *   16

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{4}`

*   *   Cl

    *   17

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{5}`

*   *   Ar

    *   18

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6}`

*   *   K

    *   19

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6} \hspace{2mm} 4s`

*   *   Ca

    *   20

    *   {math}`1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6} \hspace{2mm} 4s^{2}`
:::

% \end{enumerate}