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Size
3" × 3"
Surface
White
Made
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Size
Surface

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Mix & match pricing
  • Pick any 3: $5.25 each (3 for $15.75)
  • Pick any 5: $4.20 each (5 for $21.00)

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Free US shipping. Free international shipping with 4+ stickers, a sheet, or any tee.

Outside the US, orders of only 1–3 single stickers ship for $10.99.

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The physics

The sticker says Almost Certainly Real. It answers one sentence in a 1925 thesis.

That year, at Harvard College Observatory, Cecilia Payne finished Stellar Atmospheres. Using Meghnad Saha's new theory of how atoms ionise with temperature, she showed that the great differences between stellar spectra are mostly differences of temperature, not ingredients, and that stars look strikingly uniform in composition.

Her own numbers said something stranger: hydrogen and helium vastly outnumbered everything else. On page 188 she wrote: “The enormous abundance derived for these elements in the stellar atmosphere is almost certainly not real.” She suggested hydrogen's figure might be another aspect of its abnormal behaviour rather than a true abundance.

Henry Norris Russell, the leading authority, had written to her that it was “clearly impossible that hydrogen should be a million times more abundant than the metals”, and her caution echoes and cites him. The historian David DeVorkin reads it as a standard of evidence rather than suppression, since Russell approved the thesis, abundance table and all. How much pressure she felt is still argued over. By 1929 Russell had found hydrogen dominant by other routes, and he called her thesis “the most important previous determination of the abundance of the elements by astrophysical means.”

The label on this Sun gives today's best estimates for its surface, by mass: about 74 percent hydrogen, 25 percent helium and everything heavier in the last one percent or so. The helium figure comes from helioseismology, because the Sun's visible surface shows no usable helium lines. These are modern values, not her 1925 numbers.

Almost certainly real.

Equations

\[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]
\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
Symbols
SymbolMeaningUnit
\(n_i, n_{i+1}\) number densities of ionisation stages i and i+1 \(\mathrm{m⁻³}\)
\(n_e\) electron number density \(\mathrm{m⁻³}\)
\(g_i\) statistical weight of stage i \(\mathrm{1}\)
\(\chi_i\) ionisation energy from stage i \(\mathrm{J}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(m_e\) electron mass \(\mathrm{kg}\)
\(\Lambda\) thermal de Broglie wavelength \(\mathrm{m}\)
\(X, Y, Z\) mass fractions of hydrogen, helium, everything heavier \(\mathrm{1}\)
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