gives the values of all known properties for an atomic state or state transition.


gives the value of the specified property for the given entity.


returns the state transition with the closest wavelength or frequency specified.


returns the entity in the specified entity class with the closest wavelength or energy to the specified quantity.


returns the entities in spec that fall within the range specified between quantity1 and quantity2.


  • entity can be either an atomic state or an atomic state transition.
  • SpectralLineData["Ions"] gives a complete list of supported ions.
  • SpectralLineData["EntityClass"] returns a complete list of entity classes.
  • SpectralLineData[element] returns all entity classes for the specified element.
  • SpectralLineData[class] returns all entities for that entity class.
  • SpectralLineData[class,property] returns the property values for all entities in that entity class.
  • Entity classes are identified by their element and ionization, with the lowest level 1 corresponding to the ground state.
  • SpectralLineData["Properties"] gives a list of all properties available for atomic states.
  • Properties that do not apply or are not known in a particular case are indicated by Missing[].
  • The "Entity" property can be used to verify that an input is a valid entity or entity class for SpectralLineData.
  • Common properties for atomic states and state transitions include:
  • "Element"element
    "IonizationLevel"level of ionization starting from 1 (neutral)
    "Name"display name
    "Isotope"isotope if known
    "NISTIdentificationNumber"identification number in NIST Atomic Spectrum Database
  • Atomic state properties include:
  • "ElectronConfiguration"occupation numbers for each electron subshell
    "ElectronConfigurationString"electron configuration written in standard notation
    "Energy"energy above ground state
    "JValue"coupling constant J value
    "OrbitalL"azimuthal quantum number
    "Parity"parity value
    "PrincipalN"principal quantum number
    "QuantumNumbers"Association of quantum numbers
    "SpinS"spin quantum number
    "TermSymbol"term symbol
    "Wavenumber"wavenumber for the energy above ground state
  • Atomic state transitional properties include:
  • "CalculatedFrequency"calculated frequency of emitted or absorbed photon
    "CalculatedWavelength"calculated wavelength of emitted or absorbed photon
    "Energy"energy of emitted or absorbed photon
    "EnergyPrecision"minimum accuracy for energy
    "Frequency"observed frequency of emitted or absorbed photon
    "Intensity"relative intensity
    "LogGF"logarithm of oscillation strength accounting for degeneracy
    "LowerLevel"lower energy state of the transition
    "TransitionLevels"atomic states involved in the transition
    "TransitionProbability"probability of transition
    "TransitionStrength"absorption or emission probability
    "TransitionType"type of forbidden transitions, if applicable
    "UpperLevel"upper energy state of the transition
    "Wavelength"observed wavelength of emitted or absorbed photon
  • "TransitionType" includes several possible forbidden transitions:
  • "M1"magnetic dipole
    "E2"electric quadrapole
    "M2"magnetic quadrapole
    "E3"electric octupole
    "M3"magnetic octupole
    "M1+E2"mixed magnetic dipole and electric quadrupole
    "2P"two-photon transition
    "HF"hyperfine induced transition
    "UT"unspecified type
  • SpectralLineData[quantity,n] will return the n closest entities to the quantity. n should be a positive integer.
  • SpectralLineData[class,quantity,n] will return the n closest entities to the quantity. n should be a positive integer.
  • For atomic levels, SpectralLineData[spec,{quantity1,quantity2}] takes quantities of energy or inverse length. Quantities should be in terms of length, frequency or angular frequency for atomic lines.
  • SpectralLineData[class,Quantity[Interval[...],unit]] can also be used to query for entities within a range of values.
  • SpectralLineData[<|"Element"->element,"IonizationLevel"->i,"PrincipalN"->n,"OrbitalL"->l,"SpinS"->s,"JValue"->j|>,"Entity"] returns all levels with the requested quantum numbers. SpectralLineData[quantumnumbers] and SpectralLineData[quantumnumbers,property] can be used to query for properties of these transitions.
  • SpectralLineData[level1->level2,"Entity"], SpectralLineData[level1->level2] and SpectralLineData[level1->level2,property] can be used to find and query for atomic line transitions and their properties.
  • SpectralLineData[level->quantity,"Entity"] searches for the transition with a wavelength or frequency with the specified energy level as an upper or lower level. SpectralLineData[level->quantity] and SpectralLineData[level->quantity,property] can be used to query for properties of these transitions.
  • SpectralLineData[level->type,"Entity"] returns all transitions involving the specified energy level and the forbidden transition type. SpectralLineData[level->type] and SpectralLineData[level->type,property] can be used to query for properties of these transitions.
  • SpectralLineData[quantumnumbers1->quantumnumbers2,"Entity"], SpectralLineData[quantumnumbers1->quantumnumbers2] and SpectralLineData[quantumnumbers1->quantumnumbers2,property] can be used to find and query for atomic line transitions and their properties.
  • SpectralLineData takes a Method option. The suboption "Search" takes the options All and Automatic. Automatic searches over state transitions with observed wavelengths. All includes states that have only calculated wavelengths in searches.
  • SpectralLineData is based on a wide range of sources, with enhancement at Wolfram Research by both human and algorithmic processing.
  • [1] Ralchenko, Y., et al. "NIST Atomic Spectra Database (Version 4.0.1)." National Institute of Standards and Technology.


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Basic Examples  (5)

Discover the properties of an atomic line near 400 nm:

Find the electron configuration for the ground state of different elements:

Examine the electron configuration for excited states:

Find the energy level of an atomic state:

Find the wavelength of a spectral line between two atomic states:

Find state transitions within a specific range:

Scope  (14)

Ions  (3)

Find all valid ions:

Find all entity classes for an element:

Retrieve all entities for an ion:

Properties  (2)

Obtain a list of properties:

Find all properties of a state of neutral helium:

Listability  (1)

SpectralLineData can be run over lists of entities:

Searchability  (8)

Search for atomic state transitions by wavelength or frequency:

Find the atomic state transition closest to a specific wavelength:

Discover the 10 closest state transitions to 500 nm:

Find spectral lines within a interval of wavelengths:

Find atomic states with energies near :

Locate the two closest states:

Verify if a transition exists between two atomic states:

Locate a transition with a level and the frequency of the emitted photon:

Find all magnetic dipole transitions from a particular atomic level:

Find an atomic level based on its element and quantum numbers:

Find atomic transitions using the quantum numbers of the states:

Options  (1)

Method  (1)

Search over all wavelengths, not just observed values:

Applications  (2)

Find the wavelengths of the Balmer lines:

Plot wavelengths within the visible spectrum for carbon:

Properties & Relations  (1)

Excitation levels are ordered in terms of increasing wavenumber:

Possible Issues  (1)

Atomic states can be searched by quantities of energy and inverse length only:

State transitions can only be searched using quantities of length or frequency:

Neat Examples  (4)

Examine the visible transition lines for tungsten:

Learn about the available energy levels for all ground state atoms:

Explore the distribution of energies for the possible atomic states of tungsten:

Plot the excitation energy for the first 20 atomic states of neon:

Wolfram Research (2017), SpectralLineData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpectralLineData.html.


Wolfram Research (2017), SpectralLineData, Wolfram Language function, https://reference.wolfram.com/language/ref/SpectralLineData.html.


Wolfram Language. 2017. "SpectralLineData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpectralLineData.html.


Wolfram Language. (2017). SpectralLineData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpectralLineData.html


@misc{reference.wolfram_2024_spectrallinedata, author="Wolfram Research", title="{SpectralLineData}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/SpectralLineData.html}", note=[Accessed: 16-July-2024 ]}


@online{reference.wolfram_2024_spectrallinedata, organization={Wolfram Research}, title={SpectralLineData}, year={2017}, url={https://reference.wolfram.com/language/ref/SpectralLineData.html}, note=[Accessed: 16-July-2024 ]}