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Some "New SI" physical constants seem currently to be inaccurate

Posted 2 years ago
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Consider the current dataset value of the elementary charge:

In[1]:= Quantity["ElementaryCharge"] 10^19 // UnitConvert // First

Out[1]= 80108817/50000000

In[2]:= % // N[#, 10] &

Out[2]= 1.602176340

whereas the correct "New SI" exact value (times 10^19) is:

In[3]:= 801088317/500000000 // N[#, 10] &

Out[3]= 1.602176634

Apparently, one significant digit has been dropped, which affects all the corresponding unit conversions.

Data source: https://physics.nist.gov/cgi-bin/cuu/Value?e

As a consequence, it makes the existence of a hydrogen atom "computationally impossible":

In[1]:= {mp, me} = (*masses of proton and electron*)
 UnitConvert[#, "AtomicMassUnit"] & /@
  (Entity["Particle", #]["Mass"] & /@ {"Proton", "Electron"})

Out[1]= {1.007276274 u, 0.000548579804 u}

In[2]:= mH = (*mass of a hydrogen atom*)
 IsotopeData["H1", "AtomicMass"]

Out[2]= 1.00782503207 u

so the mass change appears to be positive:

In[3]:= mH - (mp + me)

Out[3]= 1.78*10^-7 u

which means that the hydrogen atom contains more energy than the proton and electron in total, and so the atom would not form.

The difference is pretty small, and yet positive, and one of the reasons for it is probably the inaccuracy in the value of the elementary charge constant in the current version of Mathematica's dataset (since the values are converted from eV to amu).

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