Versuch 255: Röntgenspektrometer

Needs["ErrorBarPlots`"]

Messung des Röntgenspektrums mit einem LiF-Kristall

(Subscript[spectrum, LiF])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/1a/data.dat"]

(Subscript[t, tor,a])=Quantity[5,"Seconds"]

(Subscript[plot, LiF])=With[{d=(Subscript[spectrum, LiF])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,a])]]]},{v,d}],
Joined->True,InterpolationOrder->2,Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]],0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["Röntgenspektrum via LiF\[Hyphen]Kristall",Bold]]]

Extrapolation des Grenzwinkels

(Subscript[lp, LiF])=Select[(Subscript[spectrum, LiF]),5.6≤#[[1]]≤6.2&]

(Subscript[extrapolation, LiF])=LinearModelFit[(Subscript[lp, LiF]),x,x,VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,a])]])^2)/((Sqrt[(Subscript[lp, LiF])[[All,2]]])^2))]

(Subscript[extrapolation, LiF])["ParameterTable"]

{c,Δc}=(Subscript[extrapolation, LiF])["ParameterTableEntries"][[1,1;;2]]

{m,Δm}=(Subscript[extrapolation, LiF])["ParameterTableEntries"][[2,1;;2]]

Show[(Subscript[plot, LiF]),Plot[(Subscript[extrapolation, LiF])[x],{x,5.2,6},PlotStyle->Red]]

(Subscript[β, grenz,LiF])=-(c/m) °

(Subscript[Δβ, grenz,LiF])=Sqrt[(((((c Δm)/(m^2))))^2)+(((((Δc)/m)))^2)]°

PlusMinus[NumberForm[((360 )/(2π))(Subscript[β, grenz,LiF]),2],NumberForm[((360 )/(2π))(Subscript[Δβ, grenz,LiF]),1]]

(Subscript[d, LiF])=Quantity[201.4,"Picometers"]

(Subscript[λ, LiF])[β_,Δβ_,n_:1]:={(2/n) (Subscript[d, LiF]) Sin[β],(2/n) (Subscript[d, LiF]) Cos[β]Δβ}

{(Subscript[λ, grenz,LiF]),(Subscript[Δλ, grenz,LiF])}=(Subscript[λ, LiF])[(Subscript[β, grenz,LiF]),(Subscript[Δβ, grenz,LiF])]

(({(Subscript[λ, grenz,LiF]),(Subscript[Δλ, grenz,LiF])} Quantity[30,"Kiloelectronvolts"])/(Quantity["SpeedOfLight"] ))//UnitConvert

Quantity["PlanckConstant"]//UnitConvert

Beginn der 2. Ordnung:

{((360 )/(2π))ArcSin[((Subscript[λ, grenz,LiF])/(Subscript[d, LiF]))],((360 )/(2π))((Subscript[Δλ, grenz,LiF])/(Subscript[d, LiF]))(1/(Sqrt[1-(((((Subscript[λ, grenz,LiF])/(Subscript[d, LiF]))))^2)]))}

Vermessung der K-Linien

(Subscript[t, tor,b])=Quantity[20,"Seconds"]

(Subscript[K, α])-Linie 1. Ordnung

(Subscript[data, LiF,(Subscript[K, α]),1])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/1b/1alpha/data.dat"]

(Subscript[plot, LiF,(Subscript[K, α]),1])=With[{d=(Subscript[data, LiF,(Subscript[K, α]),1])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,b])]]]},{v,d}],
Joined->True,InterpolationOrder->2,PlotStyle->LightGray,MeshStyle->ColorData[1,1],Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]]-.01,0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["(Subscript[K, α])\[Hyphen]Linie 1. Ordnung (via LiF\[Hyphen]Kristall)",Bold]]];

(Subscript[fit, LiF,(Subscript[K, α]),1])=With[{d=Select[(Subscript[data, LiF,(Subscript[K, α]),1]),9.6≤#[[1]]≤10.1&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,b])]])^2)/((Sqrt[d[[All,2]]])^2)),VarianceEstimatorFunction->(1&)]]

Show[(Subscript[plot, LiF,(Subscript[K, α]),1]),Plot[(Subscript[fit, LiF,(Subscript[K, α]),1])[x],{x,9.2,10.4}]]

(Subscript[fit, LiF,(Subscript[K, α]),1])["ParameterTable"]

{(Subscript[λ, (Subscript[K, α]),1]),(Subscript[Δλ, (Subscript[K, α]),1,fit])}=(Subscript[λ, LiF])@@((Subscript[fit, LiF,(Subscript[K, α]),1])["ParameterTableEntries"][[1,1;;2]]°)

FWHM (mit Fit-Fehler):

{(Subscript[Δλ, (Subscript[K, α]),1]),(Subscript[Δλ, (Subscript[K, α]),1,Δfit])}=2(Sqrt[2Log[2]])(Subscript[λ, LiF])@@((Subscript[fit, LiF,(Subscript[K, α]),1])["ParameterTableEntries"][[2,1;;2]]°)

(Subscript[K, β])-Linie 1. Ordnung

(Subscript[data, LiF,(Subscript[K, β]),1])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/1b/1beta/data.dat"]

(Subscript[plot, LiF,(Subscript[K, β]),1])=With[{d=(Subscript[data, LiF,(Subscript[K, β]),1])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,b])]]]},{v,d}],
Joined->True,InterpolationOrder->2,PlotStyle->LightGray,MeshStyle->ColorData[1,1],Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]]-.01,0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["(Subscript[K, β])\[Hyphen]Linie 1. Ordnung (via LiF\[Hyphen]Kristall)",Bold]]];

(Subscript[fit, LiF,(Subscript[K, β]),1])=With[{d=Select[(Subscript[data, LiF,(Subscript[K, β]),1]),8.4≤#[[1]]≤8.8&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,b])]])^2)/((Sqrt[d[[All,2]]])^2))]]

Show[(Subscript[plot, LiF,(Subscript[K, β]),1]),Plot[(Subscript[fit, LiF,(Subscript[K, β]),1])[x],{x,8,9.2}]]

(Subscript[fit, LiF,(Subscript[K, β]),1])["ParameterTable"]

{(Subscript[λ, (Subscript[K, β]),1]),(Subscript[Δλ, (Subscript[K, β]),1,fit])}=(Subscript[λ, LiF])@@((Subscript[fit, LiF,(Subscript[K, β]),1])["ParameterTableEntries"][[1,1;;2]]°)

FWHM (mit Fit-Fehler):

{(Subscript[Δλ, (Subscript[K, β]),1]),(Subscript[Δλ, (Subscript[K, β]),1,Δfit])}=2(Sqrt[2Log[2]])(Subscript[λ, LiF])@@((Subscript[fit, LiF,(Subscript[K, β]),1])["ParameterTableEntries"][[2,1;;2]]°)

(Subscript[K, α])-Linie 2. Ordnung

(Subscript[data, LiF,(Subscript[K, α]),2])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/1b/2alpha/data.dat"]

(Subscript[plot, LiF,(Subscript[K, α]),2])=With[{d=(Subscript[data, LiF,(Subscript[K, α]),2])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,b])]]]},{v,d}],
Joined->True,InterpolationOrder->2,PlotStyle->LightGray,MeshStyle->ColorData[1,1],Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]]-.01,0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["(Subscript[K, α])\[Hyphen]Linie 2. Ordnung (via LiF\[Hyphen]Kristall)",Bold]]];

(Subscript[fit, LiF,(Subscript[K, α]),2])=With[{d=Select[(Subscript[data, LiF,(Subscript[K, α]),2]),20.2≤#[[1]]≤20.6&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x}
,VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,b])]])^2)/((Sqrt[d[[All,2]]])^2))]]

Show[(Subscript[plot, LiF,(Subscript[K, α]),2]),Plot[(Subscript[fit, LiF,(Subscript[K, α]),2])[x],{x,19.8,21}]]

(Subscript[fit, LiF,(Subscript[K, α]),2])["ParameterTable"]

{(Subscript[λ, (Subscript[K, α]),2]),(Subscript[Δλ, (Subscript[K, α]),2,fit])}=(Subscript[λ, LiF])[#1,#2,2]&@@((Subscript[fit, LiF,(Subscript[K, α]),2])["ParameterTableEntries"][[1,1;;2]]°)

FWHM (mit Fit-Fehler):

{(Subscript[Δλ, (Subscript[K, α]),2]),(Subscript[Δλ, (Subscript[K, α]),2,Δfit])}=2(Sqrt[2Log[2]])(Subscript[λ, LiF])[#1,#2,2]&@@((Subscript[fit, LiF,(Subscript[K, α]),2])["ParameterTableEntries"][[2,1;;2]]°)

(Subscript[K, β])-Linie 2. Ordnung

(Subscript[data, LiF,(Subscript[K, β]),2])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/1b/2beta/data.dat"]

(Subscript[plot, LiF,(Subscript[K, β]),2])=With[{d=(Subscript[data, LiF,(Subscript[K, β]),2])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,b])]]]},{v,d}],
Joined->True,InterpolationOrder->2,PlotStyle->LightGray,MeshStyle->ColorData[1,1],Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]]-.01,0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["(Subscript[K, β])\[Hyphen]Linie 2. Ordnung (via LiF\[Hyphen]Kristall)",Bold]]];

(Subscript[fit, LiF,(Subscript[K, β]),2])=With[{d=Select[(Subscript[data, LiF,(Subscript[K, β]),2]),17.9≤#[[1]]≤18.3&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,b])]])^2)/((Sqrt[d[[All,2]]])^2))]]

Show[(Subscript[plot, LiF,(Subscript[K, β]),2]),Plot[(Subscript[fit, LiF,(Subscript[K, β]),2])[x],{x,17.2,18.6}]]

(Subscript[fit, LiF,(Subscript[K, β]),2])["ParameterTable"]

{(Subscript[λ, (Subscript[K, β]),2]),(Subscript[Δλ, (Subscript[K, β]),2,fit])}=(Subscript[λ, LiF])[#1,#2,2]&@@((Subscript[fit, LiF,(Subscript[K, β]),2])["ParameterTableEntries"][[1,1;;2]]°)

FWHM (mit Fit-Fehler):

{(Subscript[Δλ, (Subscript[K, β]),2]),(Subscript[Δλ, (Subscript[K, β]),2,Δfit])}=2(Sqrt[2Log[2]])(Subscript[λ, LiF])[#1,#2,2]&@@((Subscript[fit, LiF,(Subscript[K, β]),2])["ParameterTableEntries"][[2,1;;2]]°)

h-Bestimmung durch Extrapolation der Einsatzspannung

(Subscript[t, tor,c])=Quantity[20,"Seconds"]

va={
{Quantity[20,"Kilovolts"],Quantity[1.85,"Becquerels"]},
{Quantity[21,"Kilovolts"],Quantity[3.45,"Becquerels"]},
{Quantity[22,"Kilovolts"],Quantity[6.70,"Becquerels"]},
{Quantity[23,"Kilovolts"],Quantity[27.40,"Becquerels"]},
{Quantity[24,"Kilovolts"],Quantity[66.60,"Becquerels"]},
{Quantity[25,"Kilovolts"],Quantity[101.5,"Becquerels"]},
{Quantity[26,"Kilovolts"],Quantity[138.0,"Becquerels"]},
{Quantity[27,"Kilovolts"],Quantity[165.4,"Becquerels"]},
{Quantity[28,"Kilovolts"],Quantity[203.1,"Becquerels"]},
{Quantity[29,"Kilovolts"],Quantity[228.7,"Becquerels"]},
{Quantity[30,"Kilovolts"],Quantity[260.9,"Becquerels"]},
{Quantity[31,"Kilovolts"],Quantity[294.7,"Becquerels"]},{Quantity[32,"Kilovolts"],Quantity[316.4,"Becquerels"]},
{Quantity[33,"Kilovolts"],Quantity[353.1,"Becquerels"]},
{Quantity[34,"Kilovolts"],Quantity[378.4,"Becquerels"]},
{Quantity[35,"Kilovolts"],Quantity[407.8,"Becquerels"]}
}

(Subscript[plot, U])=With[{d=va},ErrorListPlot[
Table[{QuantityMagnitude/@v,ErrorBar[Sqrt[QuantityMagnitude[v[[2]]]/QuantityMagnitude[(Subscript[t, tor,c])]]]},{v,d}],
Joined->True,PlotRange->All,ImageSize->Full,AxesOrigin->{QuantityMagnitude[d[[1,1]]]-1,0},AxesLabel->{"U [kV]","A [Bq]"},PlotLabel->Style["Zählrate pro Spannung bei β=7.5°",Bold]]];

(Subscript[extrapolation, U])=With[{d=QuantityMagnitude/@Select[va,23≤QuantityMagnitude[#[[1]]]<27&]}, LinearModelFit[d,x,x,VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,c])]])^2)/((Sqrt[d[[All,2]]])^2))]]

Show[(Subscript[plot, U]),Plot[(Subscript[extrapolation, U])[x],{x,21.5,28},PlotStyle->Red]]

(Subscript[extrapolation, U])["ParameterTable"]

{cU,ΔcU}=(Subscript[extrapolation, U])["ParameterTableEntries"][[1,1;;2]]

{mU,ΔmU}=(Subscript[extrapolation, U])["ParameterTableEntries"][[2,1;;2]]

(Subscript[U, grenz,LiF])=Quantity[-(cU/mU),"Kilovolts"]

(Subscript[ΔU, grenz,LiF])=Quantity[Sqrt[(((((cU ΔmU)/(mU^2))))^2)+(((((ΔcU)/mU)))^2)],"Kilovolts"]

PlusMinus[NumberForm[(Subscript[U, grenz,LiF]),{3,1}],NumberForm[(Subscript[ΔU, grenz,LiF]),1]]

(Subscript[λ, 7.5°])=First[(Subscript[λ, LiF])[7.5°,0]]

UnitConvert[((Quantity["ElementaryCharge"]*{(Subscript[U, grenz,LiF]),(Subscript[ΔU, grenz,LiF])}*(Subscript[λ, 7.5°]))/(Quantity["SpeedOfLight"])),"Joules"*"Seconds"]

Elementare Strukturanalyse eines NaCl-Kristalls

Wellenlängen aus Teil 1

{(Subscript[λ, (Subscript[K, α])]),(Subscript[Δλ, (Subscript[K, α])])}={(((Subscript[λ, (Subscript[K, α]),1])+(Subscript[λ, (Subscript[K, α]),2]))/2),(1/2)(Sqrt[((Subscript[Δλ, (Subscript[K, α]),1])^2)+((Subscript[Δλ, (Subscript[K, α]),2])^2)])}

{(Subscript[λ, (Subscript[K, β])]),(Subscript[Δλ, (Subscript[K, β])])}={(((Subscript[λ, (Subscript[K, β]),1])+(Subscript[λ, (Subscript[K, β]),2]))/2),(1/2)(Sqrt[((Subscript[Δλ, (Subscript[K, β]),1])^2)+((Subscript[Δλ, (Subscript[K, β]),2])^2)])}

Spektrum des NaCl-Kristalls

(Subscript[spectrum, NaCl])=Import["/Users/jannis/Dropbox/uniself/AP2/2.2/255 Röntgenspektrometer/2/data.dat"]

(Subscript[t, tor,2])=Quantity[5,"Seconds"]

(Subscript[plot, NaCl])=With[{d=(Subscript[spectrum, NaCl])},ErrorListPlot[
Table[{v,ErrorBar[Sqrt[v[[2]]/QuantityMagnitude[(Subscript[t, tor,2])]]]},{v,d}],
Joined->True,InterpolationOrder->2,Mesh->Full,PlotRange->All,ImageSize->Full,AxesOrigin->{d[[1,1]],0},AxesLabel->{"β [°]","A [Bq]"},PlotLabel->Style["Röntgenspektrum via NaCl\[Hyphen]Kristall",Bold]]]

(Subscript[fit, NaCl,(Subscript[K, α]),1])=With[{d=Select[(Subscript[spectrum, NaCl]),7≤#[[1]]≤7.8&]},NonlinearModelFit[d,1386 Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,2])]])^2)/((Sqrt[d[[All,2]]])^2))]]

(Subscript[fit, NaCl,(Subscript[K, β]),1])=With[{d=Select[(Subscript[spectrum, NaCl]),6.2≤#[[1]]≤6.8&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,2])]])^2)/((Sqrt[d[[All,2]]])^2))]]

(Subscript[fit, NaCl,(Subscript[K, α]),2])=With[{d=Select[(Subscript[spectrum, NaCl]),14.4≤#[[1]]≤15&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,2])]])^2)/((Sqrt[d[[All,2]]])^2))]]

(Subscript[fit, NaCl,(Subscript[K, β]),2])=With[{d=Select[(Subscript[spectrum, NaCl]),12.8≤#[[1]]≤13.2&]},NonlinearModelFit[d,Max[d[[All,2]]] Exp[-(1/2)((((x-μ))^2)/(σ^2))],{{μ,Mean[d[[All,1]]]},{σ,StandardDeviation[d[[All,1]]]}},{x},
VarianceEstimatorFunction->(1&),Weights->(((Sqrt[QuantityMagnitude[(Subscript[t, tor,2])]])^2)/((Sqrt[d[[All,2]]])^2))]]

Show[(Subscript[plot, NaCl]),
Plot[(Subscript[fit, NaCl,(Subscript[K, α]),1])[x],{x,3,18},PlotRange->Full,PlotStyle->ColorData[1,2]],
Plot[(Subscript[fit, NaCl,(Subscript[K, β]),1])[x],{x,3,18},PlotRange->Full,PlotStyle->ColorData[1,3]],
Plot[(Subscript[fit, NaCl,(Subscript[K, α]),2])[x],{x,3,18},PlotRange->Full,PlotStyle->ColorData[1,4]],
Plot[(Subscript[fit, NaCl,(Subscript[K, β]),2])[x],{x,3,18},PlotRange->Full,PlotStyle->ColorData[1,5]]]

(Subscript[fit, NaCl,(Subscript[K, α]),1])["ParameterTable"]

{(Subscript[β, NaCl,(Subscript[K, α]),1]),(Subscript[Δβ, NaCl,(Subscript[K, α]),1])}=({1,(Sqrt[2Log[2]])}(Subscript[fit, NaCl,(Subscript[K, α]),1])["ParameterTableEntries"][[1;;2,1]])

(Subscript[fit, NaCl,(Subscript[K, β]),1])["ParameterTable"]

{(Subscript[β, NaCl,(Subscript[K, β]),1]),(Subscript[Δβ, NaCl,(Subscript[K, β]),1])}=({1,(Sqrt[2Log[2]])}(Subscript[fit, NaCl,(Subscript[K, β]),1])["ParameterTableEntries"][[1;;2,1]])

(Subscript[fit, NaCl,(Subscript[K, α]),2])["ParameterTable"]

{(Subscript[β, NaCl,(Subscript[K, α]),2]),(Subscript[Δβ, NaCl,(Subscript[K, α]),2])}=({1,(Sqrt[2Log[2]])}(Subscript[fit, NaCl,(Subscript[K, α]),2])["ParameterTableEntries"][[1;;2,1]])

(Subscript[fit, NaCl,(Subscript[K, β]),2])["ParameterTable"]

{(Subscript[β, NaCl,(Subscript[K, β]),2]),(Subscript[Δβ, NaCl,(Subscript[K, β]),2])}=({1,(Sqrt[2Log[2]])}(Subscript[fit, NaCl,(Subscript[K, β]),2])["ParameterTableEntries"][[1;;2,1]])

d[λ_,Δλ_,β_,Δβ_,n_:1]:={((n λ)/(2 Sin[β])),(Sqrt[(((((n Δλ)/(2 Sin[β]))))^2)+(((((n λ Cos[β]Δβ)/(2 ((Sin[β])^2)))))^2)])}

ds=Transpose[{d[(Subscript[λ, (Subscript[K, α]),1]),(Subscript[Δλ, (Subscript[K, α]),1]),(Subscript[β, NaCl,(Subscript[K, α]),1])°,(Subscript[Δβ, NaCl,(Subscript[K, α]),1])°],
d[(Subscript[λ, (Subscript[K, β]),1]),(Subscript[Δλ, (Subscript[K, β]),1]),(Subscript[β, NaCl,(Subscript[K, β]),1])°,(Subscript[Δβ, NaCl,(Subscript[K, β]),1])°],
d[(Subscript[λ, (Subscript[K, α]),2]),(Subscript[Δλ, (Subscript[K, α]),2]),(Subscript[β, NaCl,(Subscript[K, α]),2])°,(Subscript[Δβ, NaCl,(Subscript[K, α]),2])°,2],
d[(Subscript[λ, (Subscript[K, β]),2]),(Subscript[Δλ, (Subscript[K, β]),2]),(Subscript[β, NaCl,(Subscript[K, β]),2])°,(Subscript[Δβ, NaCl,(Subscript[K, β]),2])°,2]}]

{(Subscript[d, NaCl]),(Subscript[Δd, NaCl])}={Mean[ds[[1]]],(1/4)(Sqrt[Total[((ds[[2]])^2)]])}

{(Subscript[a, NaCl]),(Subscript[Δa, NaCl])}=2{(Subscript[d, NaCl]),(Subscript[Δd, NaCl])}

(Subscript[ρ, NaCl])=Quantity[2.164,(("Grams")/(("Centimeters")^3))]

(Subscript[M, NaCl])=Quantity[58.44,"Grams"]

{Avogadro,ΔAvogadro}=(1/2)((Subscript[M, NaCl])/((Subscript[ρ, NaCl])((Subscript[d, NaCl])^3))) {1,3((Subscript[Δd, NaCl])/(Subscript[d, NaCl]))}