Helium Transitions within the Visible Spectrum

Obtain and visualize the transition in terms of the energy levels for neutral helium

Examine the energies of different atomic states using the available energy level data from the NIST Atomic Spectra Database:

In[1]:=

)

ATOMIC LEVEL



energy



Out[1]=

0.×

-3

In[2]:=

)

ATOMIC LEVEL



energy



Out[2]=

19.82

Obtain the lines within the visible spectrum for neutral helium:

In[3]:=

lines=EntityList

helium I

4000

7500

SPECTRAL LINES

;lines〚;;5〛

Out[3]=



He:(1

)

⟶ (1

)

He:(1

)

⟶ (1

)

He:(1

)

⟶ (1

)

He:(1

)

⟶ (1

)

He:(1

)

⟶ (1

)



Get the upper and lower energy level for each transition as well as the resulting wavelength:

In[4]:=

linedata=EntityValuelines,

observed wavelength

lower energy level

upper energy level

;

Extract the wavelength values:

In[5]:=

wavelengths=QuantityMagnitude[linedata〚All,1〛,"Nanometers"];

Plot wavelengths within the visible spectrum for carbon:

In[6]:=

Graphics{ColorData["VisibleSpectrum"][#],Line[{{#,0},{#,1}}]}&/@wavelengths,

scene options



Out[6]=

Extract the upper and lower levels for each transition:

In[7]:=

lowerlevels=linedata〚All,2〛;upperlevels=linedata〚All,3〛;

Gather energy information for each atomic level:

In[8]:=

leveldata=EntityValueRiffle[lowerlevels,upperlevels],

name

energy

;

Obtain a list of transitions:

In[9]:=

transitions=Partition[leveldata〚All,2〛,2,2];

Determine the colors for each transition:

In[10]:=

colors=ColorData["VisibleSpectrum"][#]&/@wavelengths;

Plot each transition in terms of the energy levels of the initial and final atomic levels:

In[11]:=

coloredTooltippedLine[{{{llName_,llE_},{ulName_,ulE_}},λ_},{k_}]:={ColorData["VisibleSpectrum"][λ],Tooltip[Line[QuantityMagnitude[{{llE,k},{ulE,k}}]],llNameulName],Tooltip[Point[QuantityMagnitude[{llE,k}]],llName],Tooltip[Point[QuantityMagnitude[{ulE,k}]],ulName]}

In[12]:=

Graphics[MapIndexed[coloredTooltippedLine,Transpose[{Partition[leveldata,2],wavelengths}]],AspectRatio1/2,FrameTrue,FrameTicks{Automatic,None},FrameLabel{Quantity[None,"Electronvolts"]}]

Out[12]=

Next add in some grid lines corresponding to the energy levels within this range:

In[13]:=

alllevels=EntityList

helium I

ATOMIC LEVELS

;

Obtain the energy values:

In[14]:=

allleveldata=EntityValuealllevels,

energy

;

Select the energy levels within the range of the plot:

In[15]:=

{min,max}=MinMax[leveldata〚All,2〛]

Out[15]=

{

20.62

24.30

}

In[16]:=

subsetlevels=Select[Transpose[{alllevels,allleveldata}],min≤#〚2〛≤max&];

Plot the transitions relative to all energy levels:

In[17]:=

Graphics{MapIndexed[{colors〚First[#2]〛,Line[QuantityMagnitude[{{First[#1],First[#2]},{Last[#1],First[#2]}}]]}&,transitions],MapIndexed[coloredTooltippedLine,Transpose[{Partition[leveldata,2],wavelengths}]]},GridLines{QuantityMagnitude[subsetlevels〚All,2〛],None},

opts



Out[17]=

Examine the atomic levels lacking transitions:

In[18]:=

Complement[subsetlevels〚All,1〛,lowerlevels,upperlevels]

Out[18]=



He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He:

193922.

/cm

He:

193922.

/cm

He:

193922.

/cm

He:

193922.

/cm

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He: (1

)

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He:

195263.

/cm

He: (1

)

He: (1

)



Compare this to the number of energy levels involved in transitions within the visible spectrum:

In[19]:=

Length[Complement[subsetlevels〚All,1〛,lowerlevels,upperlevels]]

Out[19]=

In[20]:=

Length[subsetlevels]

Out[20]=

In[21]:=

Length[Union[lowerlevels,upperlevels]]

Out[21]=

Publisher Information

Contributed by: Wolfram Staff

Helium Transitions within the Visible Spectrum

Related Symbols

Publisher Information