IndexQuânticaSticker

Maria Goeppert Mayer Sticker

A Full Floor Is Magic. | Physics

\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]
$4.99 USD
$4.99 USD
Promoção Esgotado
Size
Surface

Some nuclei are unusually stable, at numbers that looked like magic. In 1949 Goeppert Mayer, and independently Jensen, Haxel and Suess, explained the magic numbers (2, 8, 20, 28, 50, 82, 126) with spin–orbit coupling. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Protons and neutrons fill energy shells in the nucleus, much like electrons in an atom. Adding strong spin-orbit coupling moves the shell gaps to the observed magic numbers 2, 8, 20, 28, 50, 82 and 126, where nuclei are unusually stable.

The sticker says A Full Floor Is Magic. Inside a nucleus, it is.

Some nuclei are unusually stable: those with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons. They became known as magic numbers, a name said to be Eugene Wigner's, because for years nobody could explain them.

Treat each nucleon as moving in a shared well and the first shells fill at 2, 8 and 20, which is what the three rings of dancers show. Beyond that, the simple picture gives the wrong numbers. In 1949 Maria Goeppert Mayer found the missing ingredient: a strong coupling between each nucleon's spin and its orbit, so that a nucleon spinning the same way it circles sits at a different energy from one spinning the other way. That splitting reshuffles the levels, and the shells close at 28, 50, 82 and 126.

As her daughter later told it, reported by Scientific American, she explained it with a ballroom of waltzers: all the couples go round the floor one way, which is the orbit, while each couple also turns, which is the spin.

Otto Haxel, Hans Jensen and Hans Suess reached the same answer independently that year. In 1963 Goeppert Mayer and Jensen shared half of the Nobel Prize in Physics and the other half went to Wigner. She was the second woman to win the physics prize, sixty years after Marie Curie.

Protons and neutrons fill their shells separately, so our dancers are all one kind. A full floor is magic.

Equations

\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]
\[\begin{gathered} V_{\ell s} = -C(r)\,\vec\ell\cdot\vec s \\ j = \ell\pm\tfrac12,\ \text{degeneracy } 2j+1 \\ \Rightarrow\ 28,\,50,\,82,\,126 \end{gathered}\]
SymbolMeaningUnit
\(E_N\) energy of oscillator shell N \(\mathrm{J}\)
\(N\) oscillator shell number \(\mathrm{1}\)
\(\hbar\omega\) oscillator level spacing \(\mathrm{J}\)
\(g_N\) states in shell N per nucleon species (spin included) \(\mathrm{1}\)
\(V_{\ell s}\) spin–orbit potential \(\mathrm{J}\)
\(C(r)\) radial strength of the spin–orbit term (with orbital and spin angular momentum measured in units of ħ) \(\mathrm{J}\)
\(\vec\ell, \vec s\) orbital and spin angular momentum, in units of ħ \(\mathrm{1}\)
\(\ell\) orbital angular momentum quantum number \(\mathrm{1}\)
\(j\) total angular momentum quantum number \(\mathrm{1}\)

Sources

  1. Goeppert Mayer (1949) On Closed Shells in Nuclei. II, Phys. Rev. 75, 1969
  2. Haxel, Jensen & Suess (1949) On the "Magic Numbers" in Nuclear Structure, Phys. Rev. 75, 1766
  3. Goeppert Mayer, Nobel Lecture (1963) The shell model
  4. NobelPrize.org — The Nobel Prize in Physics 1963 (summary)
  5. Scientific American — The last woman to win a physics Nobel (waltz analogy)
  6. Wikipedia — Nuclear shell model

Source Mayer, M. G. (1949). On Closed Shells in Nuclei. II. Physical Review 75, 1969–1970.doi.org/10.1103/PhysRev.75.1969

Field notes

Ver tudo
1 3
Ver tudo